Dynamics of Finite-Core Vortices

  • Mikhail A. Sokolovskiy
  • Jacques Verron
Part of the Atmospheric and Oceanographic Sciences Library book series (ATSL, volume 47)


In this chapter, we consider the stability of an isolated finite-core (or distributed) two-layer vortex with respect to relatively small and finite perturbations. An analogy between a distributed heton and A-symmetrical structure of discrete hetons is demonstrated. The specific features of the nonlinear stage of evolution of unstable vortices, and the interaction between two distributed hetons or antihetons are considered. The model is shown to be promising for the description of deep-convection processes,water mass mixing in the ocean, and the formation of new quasistationary vortex structures. We study the effect of external flow and of an isolated hill on heton motion. The results obtained for a three-layer, quasigeostrophic model are given; in particular, specific features of the dynamics of meddies are studied. The role of baroclinicity in the formation of the kinematic and thermohaline structure of the ocean is analyzed.


Meddies Vortex Structure Vortex Patches Topographic Vortex Potential Vorticity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Abernathey R, Marshall J, Mazloff M, Shuckburgh E (2010) Enhancement of mesoscale eddy stirring at steering levels in the Southern Ocean. J Phys Oceanogr 40(1):170–184Google Scholar
  2. 2.
    Abraham ER, Bowen MM (2002) Chaotic stirring by a mesoscale surface-ocean flow. Chaos 12(2):373–381Google Scholar
  3. 3.
    Abrashkin AA (1987) Theory of interaction between two plane vortices in a perfect fluid. Fluid Dyn 22(1):53–59Google Scholar
  4. 4.
    Abrashkin AA, Yakubovich EI (1984) Planar rotational flows of an ideal fluid. Sov Phys Dokl 29(5):370–371Google Scholar
  5. 5.
    Adcock ST, Marshall DP (2000) Interactions between geostrophic eddies and the mean circulation over large-scale bottom topography. J Phys Oceanogr 30(12):3223–3238Google Scholar
  6. 6.
    Adcroft A, Hill C, Marshal J (1997) Representation of topography by shaved cells in a height coordinate ocean mode. Mon Weather Rev 125(9):2293–2315Google Scholar
  7. 7.
    Adduce C, Cenedese C (2004) An experimental study of a mesoscale vortex colliding with topography of varying geometry in a rotating fluid. J Mar Res 62(5):611–638Google Scholar
  8. 8.
    Afanasyev YaD, Peltier WD (1998) Three-dimensional instability of anticyclonic swirling flow in rotating fluid: laboratory experiments and related theoretical predictions. Phys Fluids 10(12):3194–3202Google Scholar
  9. 9.
    Aguiar ACB, Read PL, Wordsworth RD, Salter T, Yamazaki YH (2009) A laboratory model of Saturn’s North Polar Hexagon. Icarus 206(2):755–763Google Scholar
  10. 10.
    Aiki H, Yamagata T (2000) Successive formation of planetary lenses in an intermediate layer. Geophys Astrophys Fluid Dyn 92(1):1–29Google Scholar
  11. 11.
    Akhmetov DG (2009) Vortex rings. Springer, Berlin/Heidelberg, 150 pGoogle Scholar
  12. 12.
    Alekseenko SV, Kuibin PA, Okulov VL (2007) Theory of concentrated vortices. Springer, Berlin/Heidelberg, 494 ppGoogle Scholar
  13. 13.
    Aleynik DL (1998) The structure an evolution of a meddy and Azores frontal zone in autumn 1993. Oceanology 38:312–322Google Scholar
  14. 14.
    Alford MH, Gregg MC, D’Asaro EA (2005) Mixing, 3D mapping, and Lagrangian evolution of a thermohaline intrusion. J Phys Oceanogr 35(9):1689–1711Google Scholar
  15. 15.
    Alford MH, Pinkel R (2000) Observations of overturning in the thermocline: the context of ocean mixing. J Phys Oceanogr 30(5):805–832Google Scholar
  16. 16.
    Allen JS, Samelson RM, Newberger PA (1991) Chaos in a model of quasigeostrophic flow over topography: an application of Melnikov’s method. J Fluid Mech 226:511–547Google Scholar
  17. 17.
    Allison M, Godfrey DA, Beebe RF (1990) A wave dynamical interpretation of Saturn’s Polar Hexagon. Science 247(4946):1061–1063Google Scholar
  18. 18.
    Alves JMR, Carton X, Ambar I (2011) Hydrological structure, circulation and water mass transport in the Gulf of Cadiz. Int J Geosci 2(4):432–456Google Scholar
  19. 19.
    Ambar I (1983) A shallow core of Mediterranean water off western Portugal. Deep-Sea Res 30(6A):677–680Google Scholar
  20. 20.
    Ambar I, Serra N, Neves F, Ferreira T (2008) Observations of the Mediterranean undercurrent and eddies in the Gulf of Cadiz during 2001. J Mar Syst 71:195–220Google Scholar
  21. 21.
    Amoretti M, Dukin D, Fajans J, Pozzoli R, Romé M (2001) Asymmetric vortex merger: experiments and simulations. Phys Plasmas 8(9):3865–3868Google Scholar
  22. 22.
    An BW, McDonald NR (2005) Coastal currents and eddies and their interaction with topography. Dyn Atmos Oceans 40(4):237–253Google Scholar
  23. 23.
    Antipov SV, Nezlin MV, Snezhkin EN, Trubnikov AS (1985) Rossby auto-soliton and laboratory model of Jupiter’s Great Red Spot. Sov Phys JETP 62:1097–1107Google Scholar
  24. 24.
    Antonova RA, Zhvania BI, Lominadze DG, Nanobashvili DI, Chagelishvili GD, Yan’kov VV (1996) Dynamics of dipole vortices in the interaction with a solid boundary. Plasma Phys Rep 22(9):775–782Google Scholar
  25. 25.
    Aref H (1979) Motion of three vortices. Phys Fluids 22(3):393–400Google Scholar
  26. 26.
    Aref H (1982) Point vortex motions with a center of symmetry. Phys Fluids 25(12): 2183–2187Google Scholar
  27. 27.
    Aref H (1983) Integrable, chaos and turbulent vortex motion in two-dimensional flows. Annu Rev Fluid Mech 15:345–389Google Scholar
  28. 28.
    Aref H (1984) Stirring by chaotic advection. J Fluid Mech 143:1–21Google Scholar
  29. 29.
    Aref H (1989) Three-vortex motion with zero total circulation: addendum. J Appl Math Phys (ZAMP) 40(4):495–500Google Scholar
  30. 30.
    Aref H (2002) The development of chaotic advection. Phys Fluids 14(4):1315–1325Google Scholar
  31. 31.
    Aref H (2009) Stability of relative equilibria of three vortices. Phys Fluids 21:094101. doi:10.1063/1.3216063Google Scholar
  32. 32.
    Aref H (2010) Self-similar motion of three point vortices. Phys Fluids 22:057104. doi:10.1063/1.3425649Google Scholar
  33. 33.
    Aref H, Balachandar S (1986) Chaotic advection in a Stokes flow. Phys Fluids 29(11):3515–3521Google Scholar
  34. 34.
    Aref H, Brøns M (1998) On stagnation points and streamline topology in vortex flows. J Fluid Mech 370:1–27Google Scholar
  35. 35.
    Aref H, Jones SW, Mofina S, Zawadski I (1989) Vortices, kinematics and chaos. Phys D 37(1–3):423–440Google Scholar
  36. 36.
    Aref H, Pomphrey N (1982) Integrable and chaotic motions of four vortices. I. The case of identical vortices. Proc R Soc Lond A 380(1779):359–387Google Scholar
  37. 37.
    Aref H, Rott N, Thomann H (1992) Gröbli’s solution of the three-vortex problem. Annu Rev Fluid Mech 24:1–20Google Scholar
  38. 38.
    Aref H, Stremler MA (1999) Four-vortex motion with zero total circulation and impulse. Phys Fluids 11(12):3704–3715Google Scholar
  39. 39.
    Arendt SC (1995) Steadily translating vortices in a stratified fluid. Phys Fluids 7(2):384–388Google Scholar
  40. 40.
    Arendt SC (1996) Two-dimensional vortex dynamics in a stratified barotropic fluid. J Fluid Mech 314:139–161Google Scholar
  41. 41.
    Arhan M, Carton X, Piola A, Zenk W (2002) Deep lenses of circumpolar water in the Argentine Basin. J Geophys Res 107(C1):3007. doi:10.1029/2001JC000963Google Scholar
  42. 42.
    Arhan M, Colin de Verdiére A, Mémery L (1994) The eastern boundary of the subtropical North Atlantic. J Phys Oceanogr 24(6):1295–1316Google Scholar
  43. 43.
    Armi L (1978) Some evidence for boundary mixing in the deep ocean. J Geophys Res 83(C4):1971–1979Google Scholar
  44. 44.
    Armi L, Hebert D, Oakey N, Price JF, Richardson PL, Rossby HT, Ruddick B (1989) Two year in the life of a Mediterranean salt lens. J Phys Oceanogr 19(3):354–370Google Scholar
  45. 45.
    Armi L, Stommel H (1983) Four views of a portion of the North Atlantic subtropical gyre. J Phys Oceanogr 13(5):828–857Google Scholar
  46. 46.
    Armi L, Zenk W (1984) Large lenses of highly saline Mediterranean water. J Phys Oceanogr 14(10):1560–1576Google Scholar
  47. 47.
    Arnold VI (1965) Conditions for nonlinear stability of stationary plane curvilinear flows of an ideal fluid. Sov Math Dokl 6:773–777Google Scholar
  48. 48.
    Arnold VI (1969) On an a priori estimate in the theory of hydrodynamical stability. Am Math Soc Transl 79:267–269Google Scholar
  49. 49.
    Babiano A, Boffetta G, Provenzale A, Vulpiani A (1994) Chaotic advection in point vortex models and two-dimensional turbulence. Phys Fluids 6(7):2465–2474Google Scholar
  50. 50.
    Badin G, Tandon A, Mahadevan A (2011) Lateral mixing in the pycnocline by baroclinic mixed layer eddies. J Phys Oceanogr 41(11):2080–2101Google Scholar
  51. 51.
    Baey J-M, Carton X (2002) Vortex multipoles in two-layer rotating shallow-water flow. J Fluid Mech 460:151–175Google Scholar
  52. 52.
    Baines PG (1997) Topographic effects in stratified flows. Cambridge University Press, Cambridge, 500 ppGoogle Scholar
  53. 53.
    Baines PG, Boyer DL, Xie B (2005) Laboratory simulations of coastally trapped waves with rotation, topography and stratification. Dyn Atmos Oceans 39(3–4):153–173Google Scholar
  54. 54.
    Baines PG, Smith RB (1993) Upstream stagnation points in stratified flow past obstacles. Dyn Atmos Oceans 18(1–2):105–113Google Scholar
  55. 55.
    Balasuriya S, Jones CKRT (2001) Diffusive draining and growth of eddies. Nonlinear Process Geophysics 8(4/5):241–251Google Scholar
  56. 56.
    Baker GR (1990) A study of the numerical stability of the method of contour dynamic. Phil Trans R Soc 333(1931):391–400Google Scholar
  57. 57.
    Baker-Yeboah S, Flierl GR, Sutyrin GG, Zhang Y (2010) Transformation of an Agulhas eddy near the continental slope. Ocean Sci 6:143–159. Google Scholar
  58. 58.
    Barba LA, Leonard A (2007) Emergence and evolution of tripole vortices from net-circulation initial conditions. Phys Fluids 19(1):017101. doi:10.1063/1.2409734Google Scholar
  59. 59.
    Barbosa JP, Métais O (2000) Large-eddy simulations of deep-ocean convection: analysis of the vorticity dynamics. J Turbul 1(009):1–31Google Scholar
  60. 60.
    Baringer MO, Price JF (1997) Mixing and spreading of the Mediterranean outflow. J Phys Oceanogr 27(8):1654–1677Google Scholar
  61. 61.
    Barker SJ, Crow SC (1977) The motion of two-dimensional vortex pairs in a ground effect. J Fluid Mech 82(4):659–671Google Scholar
  62. 62.
    Barnier B, Le Provost C (1993) Influence of bottom topography roughness on the jet and inertial recirculation of a mid-latitude gyre. Dyn Atmos Oceans 18(1–2):29–65Google Scholar
  63. 63.
    Basdevant C, Couder Y, Sadourny R (1984) Vortices and vortex-couples in two-dimensional turbulence, or long-lived couples are Batchelor’s couples. Lect Notes Phys 230:327–346Google Scholar
  64. 64.
    Bashmachnikov I, Carton X (2012) Surface signature of Mediterranean water eddies in the North-East Atlantic: effect of the upper ocean stratification. Ocean Sci 8:931–943. doi:10.5194/os-8-931-2012. doi: 10.5194/osd-9-2457-2012 Google Scholar
  65. 65.
    Bashmachnikov I, Mohn C, Pelegrí JL, Martíns A, Jose F, Machí F, White M (2009) Interaction of Mediterranean water eddies with Sedlo and Seine Seamounts, subtropical Northeast Atlantic. Deep-Sea Res II 56(25):2593–2605Google Scholar
  66. 66.
    Batchelor GK (1967) An introduction to fluid mechanics. Cambridge University Press, CambridgeGoogle Scholar
  67. 67.
    Batteen ML, Martinho AS, Miller HA, McClean JL (2007) A process-oriented modelling study of the coastal Canary and Iberian Current system. Ocean Model 18(1):1–36Google Scholar
  68. 68.
    Bauer L, Morikawa GK (1976) Stability of rectilinear geostrophic vortices in stationary equilibrium. Phys Fluids 19(7):929–942Google Scholar
  69. 69.
    Beal LM, Chereskin TK, Lenn YD, Elipot S (2006) The sources and mixing characteristics of the Agulhas Current. J Phys Oceanogr 36(11):2060–2074Google Scholar
  70. 70.
    Beckers M, Clercx HJH, van Heijsts GJF, Verzicco R (2002) Evolution and instability of monopolar vortices in a stratified fluid. Phys Fluids 15(4):1033–1045Google Scholar
  71. 71.
    Beckers M, van Heijst GJF (1998) The observation of a triangular vortex in a rotating fluid. Fluid Dyn Res 22(5):265–279Google Scholar
  72. 72.
    Beckmann A, Haidvogel DB (1993) Numerical simulation of flow around a tall isolated seamount. Part 1. Problem formulation and model accuracy. J Phys Oceanogr 23(8):1736–1753Google Scholar
  73. 73.
    Beckmann A, Haidvogel DB (1997) A numerical simulation of flow at Fieberling Guyot. J Geophys Res 102(C3):5595–5613Google Scholar
  74. 74.
    Beerens SP, Ridderinkhof H, Zimmerman JFE (1994) An analytical study of chaotic stirring in tidal areas. Chaos Solit Fract 4(6):1011–1029Google Scholar
  75. 75.
    Belkin IM, Emelyanov MV, Kostyanoy AG, Fedorov KN (1986) Thermohaline structure of intermediate waters of the ocean and intrathermocline eddies. In: Fedorov KN (ed) Intrathermocline eddies in the ocean. P.P. Shirshov Institute of Oceanology, Moscow, pp 8–34 (in Russian)Google Scholar
  76. 76.
    Belkin IM, Kostyanoy AG (1992) Intrathermocline eddies in the Word ocean and their regional peculiarities. In: Barenblatt GI, Seidov DG, Sutyrin GG (eds) Coherent structures and self-organisation of currents in the ocean. Nauka, Moscow, pp 112–127 (in Russian)Google Scholar
  77. 77.
    Benilov ES (2000) The dynamics of a near-surface vortex in a two-layer ocean on the beta-plane. J Fluid Mech 420:277–299Google Scholar
  78. 78.
    Benilov ES (2001) Baroclinic instability of two-layer flows over one-dimensional bottom topography. J Phys Oceanogr 31(8):2019–2025Google Scholar
  79. 79.
    Benilov ES (2003) Instability of quasi-geostrophic vortices in a two-layer ocean with a thin upper layer. J Fluid Mech 475:303–331Google Scholar
  80. 80.
    Benilov ES (2005) Stability of a two-layer quasigeostrophic vortex over axisymmetric localized topography. J Phys Oceanogr 35(1):2019–2025Google Scholar
  81. 81.
    Benilov ES (2005) On the stability of oceanic vortices: a solution to the problem? Dyn Atmos Oceans 40(3):133–149Google Scholar
  82. 82.
    Bennett A (2006) Lagrangian fluid dynamics. Cambridge University Press, Cambridge, 310 ppGoogle Scholar
  83. 83.
    Berestov AL (1979) Solitary Rossby waves. Izv Atmos Ocean Phys 15:443–447Google Scholar
  84. 84.
    Berestov AL (1981) Some new solutions for the Rossby solitons. Izv Atmos Ocean Phys 17:82–87Google Scholar
  85. 85.
    Berestov AL (1985) Dispersion relationships for the Rossby solitons. Izv Atmos Ocean Phys 21:332–334Google Scholar
  86. 86.
    Berestov AL, Monin AS (1980) Solitary Rossby waves. Adv Mech 3:3–34Google Scholar
  87. 87.
    Birkhoff G (1960) Hydrodynamics. A study in logic, fact, and similitude. 2nd edn. revised and enlarged. Princeton University Press, Princeton, 184 ppGoogle Scholar
  88. 88.
    Billant P, Chomaz J-M (2000) Experimental evidence for a new instability of a vertical columnar vortex pair in a strongly stratified fluid. J Fluid Mech 418:167–188Google Scholar
  89. 89.
    Blackmore D, Ting L, Knio O (2007) Studies of perturbed three vortex dynamics. J Math Phys. doi:10.1063/1.2428272Google Scholar
  90. 90.
    Bogomolov VA (1977) Vorticity dynamics on a sphere. Fluid Dyn 6(6):863–870Google Scholar
  91. 91.
    Bogomolov VA (1985) On motion on a rotating sphere. Izv Atmos Ocean Phys 21:391–396Google Scholar
  92. 92.
    Bograd SJ, Rabinovich AB, LeBlond PH, Shore JA (1997) Observations of seamount-attached eddies in the North Pacific. J Geophys Res 102(C6):12441–12456Google Scholar
  93. 93.
    Bolsinov AV, Fomenko AT (1995) Orbital equivalence of integrable Hamiltonian systems with two degrees of freedom. A classification theorem. I. Sbornik: Mathematics 81(2):421–466Google Scholar
  94. 94.
    Bord EG (2006) On the nonlinear disturbances of vortex polygon. Russ Sci J Nonlinear Dyn 2(3):353–360 (in Russian)Google Scholar
  95. 95.
    Borenäs KM, Wåhlin AK, Ambar I, Serra N (2002) The Mediterranean outflow splitting—a comparison between theoretical models and CANIGO data. Deep-Sea Res II 49(19):4195–4205Google Scholar
  96. 96.
    Borth H (1999) Von Kármánsche Wirbelstraßen und barokline Jetströme in einem 2-Schichten Kanal auf der beta-Ebene. PhD thesis, University of Bremen, Germany, 1999 AWI Rep. 96, 147 ppGoogle Scholar
  97. 97.
    Borisov AV, Bolsinov AV, Mamaev IS (1999) Lie algebras in vortex dynamics and celestial mechanics: 4. Regul Chaotic Dyn 4(1):23–50Google Scholar
  98. 98.
    Borisov AV, Lebedev VG (1998) Dynamics of three vortices on a plane and a sphere: 2. General compact case. Regul Chaotic Dyn 3(2):99–114Google Scholar
  99. 99.
    Borisov AV, Lebedev VG (1998) Dynamics of three vortices on a plane and a sphere: 3. Noncompact case. Problem of collapse and scattering. Regul Chaotic Dyn 3(4):74–86Google Scholar
  100. 100.
    Borisov AV, Kilin AA, Mamaev IS (2005) Absolute and relative choreographies in the problem of the motion of point vortices in a plane. Dokl Math 71(1):139–144Google Scholar
  101. 101.
    Borisov AV, Kilin AA, Mamaev IS (2006) Transition to chaos in dynamics of four point vortices on a plane. Dokl Phys 51(5):262–267Google Scholar
  102. 102.
    Borisov AV, Mamaev IS (1999) Poisson structures and Lie algebras in the Hamiltonian mechanics. Publisher House Udmurt University, Izhevsk, 464 pp (in Russian)Google Scholar
  103. 103.
    Borisov AV, Mamaev IS (2005) Mathematical methods in the dynamics of vortex structures. Institute of Computer Sciences, Moscow–Izhevsk, 368 pp (in Russian)Google Scholar
  104. 104.
    Borisov AV, Mamaev IS, Kilin AA (2004) Absolute and relative choreographies in the problem of point vortices moving on a plane. Regul Chaotic Dyn 9(2):101–111Google Scholar
  105. 105.
    Borisov AV, Pavlov AE (1998) Dynamics and statics of vortices on a plane and a sphere: 1. Regul Chaotic Dyn 3(1):28–39Google Scholar
  106. 106.
    Bower AS (1991) A simple kinematic mechanism for mixing fluid parcels across a meandering jet. J Phys Oceanogr 21(1):173–182Google Scholar
  107. 107.
    Bower AS, Armi L, Ambar I (1995) Direct evidence of the meddy formation off south-western coast of Portugal. Deep-Sea Res 42:1621–1630Google Scholar
  108. 108.
    Bower AS, Armi L, Ambar I (1997) Lagrangian observations of meddy formation during a Mediterranean Undercurrent Seeding Experiment. J Phys Oceanogr 27(12):2545–2575Google Scholar
  109. 109.
    Bower AS, Rossby T (1989) Evidence of cross-frontal exchange processes in the Gulf Stream based on isopycnal RAFOS float data. J Phys Oceanogr 19(6):1177–1190Google Scholar
  110. 110.
    Bower AS, Rossby HT, Lillibridge JL (1985) The Gulf Stream—barrier or blender? J Phys Oceanogr 15(1):24–32Google Scholar
  111. 111.
    Bower AS, Serra N, Ambar I (2002) Structure of the Mediterranean undercurrent and Mediterranean water spreading around the southwestern Iberian Peninsula. J Geophys Res 107(C10):3161. doi:10.1029/2001JC001007Google Scholar
  112. 112.
    Boyer DL, Davies PA (2000) Laboratory studies of orographic effects in rotating and stratified flows. Annu Rev Fluid Mech 32:165–202Google Scholar
  113. 113.
    Boyland P, Stremler M, Aref H (2003) Topological fluid mechanics of point vortex motions. Phys D 175(1–2):69–95Google Scholar
  114. 114.
    Bracco A, Pedlosky J (2003) Vortex generation by topography in locally unstable baroclinic flows. J Phys Oceanogr 33(1):207–219Google Scholar
  115. 115.
    Bracco A, Pedlosky J, Pickart RS (2008) Eddy formation near the West Coast of Greenland. J Phys Oceanogr 38(9):1992–2002Google Scholar
  116. 116.
    Bracco A, Provenzali A, Scheuring I (2000) Mesoscale vortices and the padadox of the plancton. Proc R Soc Lond B 267:1795–1800Google Scholar
  117. 117.
    Brandt LK, Cichocki TK, Nomura KK (2010) Asymmetric vortex merger: mechanism and criterion. Theor Comput Fluid Dyn 24:163–167Google Scholar
  118. 118.
    Brandt LK, Nomura KK (2006) The physics of vortex merger: further insight. Phys Fluids 18:051701. doi:10.1063/1.2201474Google Scholar
  119. 119.
    Brickman D (1995) Heat flux partitioning in deep-ocean convection. J Phys Oceanogr 25(11), part 1:2609–2623Google Scholar
  120. 120.
    Brown MG (1990) Are SOFAR float trajectories chaotic? J Phys Oceanogr 20(1):139–149Google Scholar
  121. 121.
    Brunner-Suzuki A-MEG, Sundermeyer MA, Lelong M-P (2012) Vortex stability in a large-scale internal wave shear. J Phys Oceanogr 42(10):1668–1683Google Scholar
  122. 122.
    Brutyan MA, Krapivskii PL (1988) Hamiltonian formulation and fundamental conservation laws for a model of small elliptical vortices. J Appl Math Mech 52(1):133–136Google Scholar
  123. 123.
    Bubnov VA (1971) Structure and dynamics of the Mediterranean waters in the Atlantic Ocean. Ocean Res 22:220–286 (in Russian)Google Scholar
  124. 124.
    Budyansky MV, Uleysky MYu, Prants SV (2002) Fractals and dynamic traps in the simplest model of chaotic advection with a topographic vortex. Dokl Earth Sci 387(8):929–932Google Scholar
  125. 125.
    Budyansky MV, Uleysky MYu, Prants SV (2004) Chaotic scattering, transport, and fractals in a simple hydrodynamic flow. J Exp Theor Phys 99(5):1018–1027Google Scholar
  126. 126.
    Budyansky MV, Uleysky MYu, Prants SV (2004) Hamiltonian fractals and chaotic scattering of passive particles by a topographical vortex and an alternating current. Phys D 195(3–4):369–378Google Scholar
  127. 127.
    Budyansky MV, Uleysky MYu, Prants SV (2007) Lagrangian coherent structures, transport and chaotic mixing in simple kinematic ocean models. Commun Nonlinear Sci Numer Simul 12(1):31–44Google Scholar
  128. 128.
    Budyansky MV, Uleysky MYu, Prants SV (2009) Detecting barriers to cross-jet Lagrangian transport and its destruction in a meandering flow. Phys Rev E 79(5):056215. doi:10.1103/PhysRevE.79.056215Google Scholar
  129. 129.
    Burbea J (1982) On patches of uniform vorticity in a plane of irrotational flow. Arch Ration Mech Anal 77:349–358Google Scholar
  130. 130.
    Burbea J (1982) Motions of vortex patches. Lett Math Phys 6:1–16Google Scholar
  131. 131.
    Burbea J, Landau M (1982) The Kelvin waves in vortex dynamics and their stability. J Comput Phys 45(1):127–156Google Scholar
  132. 132.
    Byshev VI (1992) Properties of an intra-thermocline lens on a subpolar front in the North Atlantic. Oceanology 32(4):701–707Google Scholar
  133. 133.
    Cabral HE, Schmidt DS (2000) Stability of relative equilibria in the problem on N+1 vortices. SIAM J Math Anal 31(2):231–250Google Scholar
  134. 134.
    Capéran P, Verron J (1988) Numerical simulation of a physical experiment on two-dimensional vortex merger. Fluid Dyn Res 3(1–4):87–92Google Scholar
  135. 135.
    Carmack EC, Kulikov EA (1998) Wind-forced upwelling and internal Kelvin wave generation in Mackenzie Canyon, Beaufort Sea. J Geophys Res 103(C9):18447–18458Google Scholar
  136. 136.
    Carnevale GF, Kloosterziel RC (1994) Emergence and evolution of triangular vortices. J Fluid Mech 259:305–331Google Scholar
  137. 137.
    Carnevale GF, Kloosterziel RC, van Heijst GJF (1991) Propagation of barotropic vortices over topography in a rotating tank. J Fluid Mech 233:119–139Google Scholar
  138. 138.
    Carnevale GF, Purini R, Orlandi P, Cavazza P (1995) Barotropic quasi-geostrophic f-plane flow over anisotropic topography. J Fluid Mech 285:329–347Google Scholar
  139. 139.
    Carnevale GF, Vallis GK, Purini R, Briscolini M (1988) The role of initial conditions in flow stability with an application to modons. Phys Fluids 31(9):2567–2572Google Scholar
  140. 140.
    Carnevale GF, Velasco Fuentes OU, Orlandi P (1997) Inviscid dipole-vortex rebound from a wall or coast. J Fluid Mech 351:75–103Google Scholar
  141. 141.
    Carr LE III, Williams RT (1989) Barotropic vortex stability to perturbations from axisymmetry. J Atmos Sci 46(20):3177–3191Google Scholar
  142. 142.
    Carton XJ (1992) On the merger of shielded vortices. Europhys Lett 18(8):697–703Google Scholar
  143. 143.
    Carton XJ (2001) Hydrodynamical modelling of oceanic vortices. Surv Geophys 22(3):179–263Google Scholar
  144. 144.
    Carton XJ (2009) Instability of surface quasigeostrophic vortices. J Atmos Sci 66(4):1051–1062Google Scholar
  145. 145.
    Carton X, Chérubin L, Paillet J, Morel Y, Serpette A, Le Cann B (2002) Meddy coupling with a deep cyclone in the Gulf of Cadiz. J Mar Syst 32(1–3):13–42Google Scholar
  146. 146.
    Carton XJ, Corréard SM (1999) Baroclinic tripolar vortices: formation and subsequent evolution. In: Sorensen JN, Hopfinger EJ, N Aubry (eds) Simulation and identification of organized structures in flows: IUTAM/SIMFLOW symposium. Dordrecht, Kluwer, pp 181–190Google Scholar
  147. 147.
    Carton XJ, Daniault N, Alves J, Chérubin L, Ambar I (2010) Meddy dynamics and interaction with neighboring eddies southwest of Portugal: observations and modeling. J Geophys Res. doi:10.1029/2009JC005646Google Scholar
  148. 148.
    Carton XJ, Flierl GR, Perrot X, Meunier T, Sokolovskiy MA (2010) Explosive instability of geostrophic vortices. Part 1: baroclinic instability. Theor Comput Fluid Dyn 24(1–4):125–130Google Scholar
  149. 149.
    Carton XJ, Flierl GR, Polvani LM (1989) The generation of tripoles from unstable axisymmetric isolated vortex structures. Europhys Lett 9(4):339–344Google Scholar
  150. 150.
    Carton XJ, Legras B (1994) The life-cycle of tripoles in two-dimensional incompressible flows. J Fluid Mech 267:51–82Google Scholar
  151. 151.
    Carton XJ, Meunier T, Flierl GR, Perrot X, Sokolovskiy MA (2010) Explosive instability of geostrophic vortices. Part 2: parametric instability. Theor Comput Fluid Dyn 24(1–4):131–135Google Scholar
  152. 152.
    Carton XJ, McWilliams JC (1989) Barotropic and baroclinic instabilities of axisymmetric vortices in a quasigeostrophic model. In: Nihoul JCJ, Jamart BM (eds) Mesoscale/synoptic coherent structures in geophysical turbulence. Amsterdam/Oxford/New York/Tokyo, Elsevier, pp 225–244Google Scholar
  153. 153.
    Cartwright JHE, Feingold M, Piro O (1996) Chaotic advection in three-dimensional unsteady incompressible laminar flow. J Fluid Mech 366:259–284Google Scholar
  154. 154.
    Cenedese C (2002) Laboratory experiments on mesoscale vortices colliding with a seamount. J Geophys Res 107(C6). doi:10.1029/2000JC000599Google Scholar
  155. 155.
    Cenedese C, Linden PF (1999) Cyclone and anticyclone formation in a rotating stratified fluid over a sloping bottom. J Fluid Mech 381:199–223Google Scholar
  156. 156.
    Cenedese C, Marshall J, Whitehead JA (2004) A laboratory model of thermocline depth and exchange fluxes across circumpolar fronts. J Phys Oceanogr 34(3):656–667Google Scholar
  157. 157.
    Cenedese C, Whitehead JA (2000) Eddy-shedding from a boundary current around a cape over a sloping bottom. J Phys Oceanogr 30(7):1514–1531Google Scholar
  158. 158.
    Cerretelli C, Williamson CHK (2003) The physical mechanism for vortex merging. J Fluid Mech 475:41–77Google Scholar
  159. 159.
    Cerretelli C, Williamson CHK (2003) A new family of uniform vortices relating to vortex configurations before merging. J Fluid Mech 493:219–229Google Scholar
  160. 160.
    Cessi P, Ierley G, Young W (1987) A model of the inertial recirculation driven by potential vorticity anomalies. J Phys Oceanogr 17(10):1640–1652Google Scholar
  161. 161.
    Cessi P, Young WR, Polton JA (2006) Control of large-scale heat transport by small-scale mixing. J Phys Oceanogr 36(10):1877–1896Google Scholar
  162. 162.
    Chao S-Y, Shaw P-T (1999) Close interactions between two pairs of heton-like vortices under sea ice. J Geophys Res 104(C10):23591–23605Google Scholar
  163. 163.
    Chao S-Y, Shaw P-T (1999) Fission of heton-like vortices under sea ice. J Oceanogr 55(1):65–78Google Scholar
  164. 164.
    Chao S-Y, Shaw P-T (2000) Slope-enhanced fission of salty hetons under sea ice. J Phys Oceanogr 30(11):2866–2882Google Scholar
  165. 165.
    Chao S-Y, Shaw P-T (2003) Heton shedding from submarine-canyon plumes in an Arctic boundary current system: sensitivity to the undercurrent. J Phys Oceanogr 33(9):2032–2044Google Scholar
  166. 166.
    Chaplygin SA (1899) On a pulsating cylindrical vortex. Trans Phys Sect Imp Mosc Soc Frends Nat Sci 10:13–22 (in Russian). English translation in: Regul Chaotic Dyn 2007, 12(1):101–116Google Scholar
  167. 167.
    Chaplygin SA (1903) One case of vortex motion in fluid. Trans Phys Sect Imp Mosc Soc Frends Nat Sci 11(2):11–12 (in Russian)Google Scholar
  168. 168.
    Charlton AJ, O’Neil A, Lahoz WA, Berrisford P (2005) The splitting of the stratospheric polar vortex in the Southern Hemisphere, September 2002: dynamical evolution. J Atmos Sci 62(3):590–602Google Scholar
  169. 169.
    Charney JG (1963) Numerical experiments in atmospheric hydrodynamics. In: Metropolis NC, Taub AH, Todd J, Tompkins CB (eds) Proceedings of symposia in applied mathematics “Experimental arithmetic high speed computing and mathematics”. Am Math Soc 15:289–310Google Scholar
  170. 170.
    Chefranov SG (2001) Centrifugal-dissipative instability of Rossby vortices and their cyclonic-anticyclonic asymmetry. J Exp Theor Phys Lett 73(6):274–278Google Scholar
  171. 171.
    Chen LG, Dewar WK (1993) Intergure communication in a three-layer model. J Phys Oceanogr 23(5):855–878Google Scholar
  172. 172.
    Chenciner A, Gerver J, Montgomery R, Simó C (2002) Simple choreographic motions of N bodies: a preliminary study. In: Newton P, Holmes P, Weinstein A (eds) Geometry, mechanics, and dynamics: volume in honor of the 60th birthday of J.E. Marsden, part III. Springer, New York, pp 287–308Google Scholar
  173. 173.
    Chernyshenko SI (1988) The asymptotic form of the stationary separated circumfluence of a body at hight Reynolds numbers. J Appl Math Mech 52(6):746–753Google Scholar
  174. 174.
    Chernyshenko S (1993) Stratified Sadovskii flow in a channel. J Fluid Mech 250:423–431Google Scholar
  175. 175.
    Chérubin LM, Carton X, Dritschel DG (2007) Vortex dipole formation by baroclinic instability of boundary currents. J Phys Oceanogr 37(6):1661–1667Google Scholar
  176. 176.
    Chérubin LM, Carton X, Paillet J, Morel Y, Serpette A (2000) Instability of the Mediterranean water undercurrents southwest of Portugal: effects of baroclinicity and topography. Oceanol Acta 23(5):551–573Google Scholar
  177. 177.
    Chérubin LM, Morel Y, Chassignet EP (2006) Loop current ring shedding: the formation of cyclones and the effect of topography. J Phys Oceanogr 36(4):569–591Google Scholar
  178. 178.
    Chérubin L, Serpette A, Carton X, Paillet J, Connan O, Morin P, Rousselet R, Le Cann B, Le Corre P, Labasque T, Corman D, Poete N (1977) Descriptive analysis of the hydrology and currents on the Iberian shelf from Gibraltar to cape Finisterre: preliminary results of the INTERAFOS and SEMANE experiments. Ann Hydrogr 21(768):5–81Google Scholar
  179. 179.
    Chirikov BV (1979) A universal instability of many-dimensional oscillator systems. Phys Rep 52(5):263–379Google Scholar
  180. 180.
    Christiansen JP, Zabusky NJ (1973) Instability, coalescence and fission of finite-area vortex structures. J Fluid Mech 61(part 2):219–243Google Scholar
  181. 181.
    Corréard SM, Carton XJ (1999) Formation and stability of tripolar vortices in stratified geostrophic flows. Il Nuovo Cim 22C(6):767–777Google Scholar
  182. 182.
    Couder Y, Basdevant C (1986) Experimental and numerical study of vortex couples in two-dimensional flows. J Fluid Mech 173:225–251Google Scholar
  183. 183.
    Cresswell GR (1982) The coalescence of two East Australian Current warm-core eddies. Science 215(4529):161–164Google Scholar
  184. 184.
    Crow SC (1970) Stability theory for a pair of trailing vortices. AIAA J 8(12):2172–2179Google Scholar
  185. 185.
    Crowdy DG (1999) A class of exact multipolar vortices. Phys Fluids 11(9):2556–2564Google Scholar
  186. 186.
    Crowdy DG (2002) The construction of exact multipolar equilibria of the two-dimensional Euler equations. Phys Fluids 14(1):257–267Google Scholar
  187. 187.
    Crowdy D (2002) Exact solutions for rotating vortex arrays with finite-area cores. J Fluid Mech 469:209–235Google Scholar
  188. 188.
    Crowdy D (2004) Explicit solutions for a steady vortex-wave interaction. J Fluid Mech 513:161–170Google Scholar
  189. 189.
    Crowdy D, Duchemin L (2005) The effect of solid boundaries on pore shrinkage in Stokes flow. J Fluid Mech 531:359–379Google Scholar
  190. 190.
    Crowdy D, Marshall J (2005) Analytical solutions for rotating vortex arrays involving multiple vortex patches. J Fluid Mech 523:307–337Google Scholar
  191. 191.
    Crowdy D, Sunara A (2007) Contour dynamics in complex domains. J Fluid Mech 593:235–254Google Scholar
  192. 192.
    Crowdy D, Tanveer S, Vasconcelos G (2005) On a pair of interacting bubbles in planar Stokes flow. J Fluid Mech 541:231–261Google Scholar
  193. 193.
    Cushman-Roisin B (1989) On the role of filamentation in the merging of enticyclonic lenses. J Phys Oceanogr 19(2):253–258Google Scholar
  194. 194.
    Cushman-Roisin B (1994) Introduction to geophysical fluid dynamics. Prentice Hall, New York, 320 ppGoogle Scholar
  195. 195.
    Cushman-Roisin B (1995) Effects of horizontal advection on upper ocean mixing: a case of frontogenesis. J Phys Oceanogr 11(10):1345–1356Google Scholar
  196. 196.
    Cushman-Roisin B, Beckers J-M (2011) Introduction to geophysical fluid dynamics. Physical and numerical aspects, 2nd edn. Academic Press, Elsevier Inc., Amstardam/Boston/Heidelberg/London/New York/Oxford/Paris/San Diego/San Francisco/Singapore/Sydney/Tokyo, 828 ppGoogle Scholar
  197. 197.
    Cushman-Roisin B, Sutyrin GG, Tang B (1992) Two-layer geostrophic dynamics: 1. Governing equations. J Phys Oceanogr 22(2):117–127Google Scholar
  198. 198.
    Danabasoglu G, McWilliams JC, Gent PR (1994) The role of mesoscale tracer transports in the global ocean circulation. Science 264(5162):1123–1126Google Scholar
  199. 199.
    Danilov S, Gryanik V, Olbers D (1998) Equilibration and lateral spreading of a strip-shaped convection region. In: Alfred-Wegener-Institut für Polar- und Meeresforschung, Report 86, 66 ppGoogle Scholar
  200. 200.
    Danilov S, Gryanik V, Olbers D (2001) Equilibration and lateral spreading of a strip-shaped convection region. J Phys Oceanogr 31(4):1075–1087Google Scholar
  201. 201.
    Darnitskiy VB (2010) Oceanological processes near underwater mountains and ridges of open ocean. Vladivostok, FSUE “TINRO-Center”, 200 pp (in Russian)Google Scholar
  202. 202.
    Davey MK (1977) Baroclinic instability in a fluid with three layers. J Atmos Sci 34(8):1224–1234Google Scholar
  203. 203.
    Davey MK (1978) Recycling flow over bottom topography in a rotating annulus. J Fluid Mech 87(3):497–520Google Scholar
  204. 204.
    Davey MK, Hurst RGA, Johnson ER (1993) Topographic eddies in multilayer flow. Dyn Atmos Oceans 18(1–2):1–27Google Scholar
  205. 205.
    Davies I, Truman A, Williams D (1983) Classical periodic solutions of the equal-mass 2n-body problem, b-ion problem and the n-electron problem. Phys Lett 99A(1):15–18Google Scholar
  206. 206.
    Davies PA (1972) Experiments on Taylor columns in rotating stratified fluids. J Fluid Mech 54(4):691–717Google Scholar
  207. 207.
    Davies PA, Guo Y, Rotenberg E (2001) Laboratory model studies of Mediterranean outflow adjustment in the Gulf of Cadiz. Deep-Sea Res Part II 49(19):4207–4223Google Scholar
  208. 208.
    Davies PA, Rahm L (1982) The interaction between topography and a nonlinearly stratified rotating fluid. Phys Fluids 25(11):1931–1934Google Scholar
  209. 209.
    Davies TV (1948) Rotatory flow on the surface of the earth. Part I. Cyclostrophic motion. Philos Mag Ser 7 39(293):482–491Google Scholar
  210. 210.
    Deem GS, Zabusky NJ (1978) Vortex waves: stationary ’V-states’, intarctions, recurrence, and breaking. Phys Rev Lett 40(13):859–862Google Scholar
  211. 211.
    De-Hai L (1994) Quasi-resonant interactions among barotropic Rossby waves with two-wave topography and low frequency dynamics. Geophys Astrophys Fluid Dyn 76(1–4):145–163Google Scholar
  212. 212.
    De-Hai L, Yan L (2001) Dynamics of meddies interacted with a seamount in a 1.5 layer model. J Hydrodyn Ser B 3:93–99Google Scholar
  213. 213.
    del-Castillo-Negrete D, Greene JM, Morrison PJ (1996) Area preserving nontwist maps: periodic orbits and transition to chaos. Phys D 91(1–2):1–23Google Scholar
  214. 214.
    del-Castillo-Negrete D, Morrison PJ (1993) Chaotic transport by Rossby waves in shear flow. Phys Fluids A 5(4):948–965Google Scholar
  215. 215.
    de Verdiere AC (1992) On the southward motion of Mediterranean salt lenses. J Phys Oceanogr 22(4):413–420Google Scholar
  216. 216.
    Dewar WK (1988) Ventilating beta plane lenses. J Phys Oceanogr 18(8):1193–1201Google Scholar
  217. 217.
    Dewar WK (2002) Convection in small basins. J Phys Oceanogr 32(10):2766–2788Google Scholar
  218. 218.
    Dewar WK (2002) Baroclinic eddy interaction with isolated topography. J Phys Oceanogr 32(10):2789–2805Google Scholar
  219. 219.
    Dhanak MR, Marshall MP (1993) Motion of an elliptic vortex under applied periodic strain. Phys Fluids A5(5):1224–1230Google Scholar
  220. 220.
    DiBattista MT, Majda AJ (2000) An equilibrium statistical theory for large-scale features of open-ocean deep convection. J Phys Oceanogr 30(6):1325–1353Google Scholar
  221. 221.
    DiBattista MT, Majda AJ (2001) Equilibrium statistical predictions for baroclinic vortices: the role of angular momentum. Theor Comput Fluid Dyn 14(5):293–322Google Scholar
  222. 222.
    DiBattista MT, Majda AJ, Marshall A (2002) A statistical theory for the “pathiness” of open-ocean deep convection: the effect of preconditioning. J Phys Oceanogr 32(2):599–626Google Scholar
  223. 223.
    Dijkstra HA (2005) Nonlinear physical oceanography: a dynamical systems approach to the large scale ocean circulation and El Niño, 2nd reversed and enlarged edn. Springer Science+Business media, New York, 532 pGoogle Scholar
  224. 224.
    Dikarev SN (1992) Deep convection—the process of deep water formation in the open sea. In: Barenblatt GI, Seidov DG, Sutyrin GG (eds) Coherent structures and self-organisation of currents in the ocean. Nauka, Moscow, pp 145–155 (in Russian)Google Scholar
  225. 225.
    Dolzhanskii FV, Krymov VA, Manin DYu (1990) Stability and vortex structures of quasi-two-dimensional shear flows. Phys Usp (Adv Phys Sci) 33(7):495–520Google Scholar
  226. 226.
    Doronina TN (1994) On the structure of an intense baroclinic vortex in three-dimensional shearing motions. Dokl (Trans) RAS Earth Sci Sect 339(4):528–532Google Scholar
  227. 227.
    Doronina TN (1995) The structure of circulation cells in intense baroclinic vortices in a current with a velocity shift and the advective transport of a solute. Izv Atmos Ocean Phys 31(2):223–232Google Scholar
  228. 228.
    Doronina TN (1997) Interaction of baroclinic point vortices in quasi-geostrophic barotropic and baroclinic shearing flows. Oceanology 37(4):454–460Google Scholar
  229. 229.
    Doronina T, Gryanik V, Olbers D, Warncke T (1998) A 3D heton mechanism of lateral spreading in lacalized convection in a rotating stratified fluid. Alfred-Wegener-Institut für Polar- und Meeresforschung, Report 87, 84 ppGoogle Scholar
  230. 230.
    Drillet Y, Bourdallé-Badie R, Siefridt L, Le Provost C (2005) Meddies in the Mercator North Atlantic and Mediterranean Sea eddy-resolving model. J Geophys Res 110:C03016. doi:10.1029/2003JC002170Google Scholar
  231. 231.
    Dritschel DG (1985) The stability and energetics of corotating uniform vortices. J Fluid Mech 157:95–134Google Scholar
  232. 232.
    Dritschel DG (1986) The nonlinear evolution of rotating configurations of uniform vorticty. J Fluid Mech 172:157–182Google Scholar
  233. 233.
    Dritschel DG (1988) Contour surgery: a topological reconnection scheme for extended integrations using contour dynamics. J Comput Phys 77(1):240–266Google Scholar
  234. 234.
    Dritschel DG (1988) The repeated filamentation of two-dimensional vorticity interfaces. J Fluid Mech 194:511–547Google Scholar
  235. 235.
    Dritschel DG (1989) On the stabilization of a two-dimensional vortex strip by adverse shear. J Fluid Mech 206:193–221Google Scholar
  236. 236.
    Dritschel DG (1990) The stability of elliptical vortices in an external straining flow. J Fluid Mech 210:223–261Google Scholar
  237. 237.
    Dritschel DG (1995) A general theory for two-dimensional vortex interactions. J Fluid Mech 293:269–303Google Scholar
  238. 238.
    Dritschel DG (1998) On the persistence of non-axisymmetric vortices in inviscid two-dimensional flows. J Fluid Mech 371:141–155Google Scholar
  239. 239.
    Dritschel D, Legras B (1998) Modeling oceanic and atmospheric vortices. Phys Today 46(3):44–51Google Scholar
  240. 240.
    Dritschel DG, Waugh DW (1992) Quantification of the inelastic interaction of inequal vortices in two-dimensional vortex dynamics. Phys Fluids A4(8):1737–1744Google Scholar
  241. 241.
    Eckart C (1948) An analysis of the stirring and mixing processes in incompressible fluid. J Mar Res 7(3):265–275Google Scholar
  242. 242.
    Eckart C (1960) Hydrodynamics of oceans and atmospheres. Pergamon Press, New York, 290 ppGoogle Scholar
  243. 243.
    Eckhardt B (1988) Integrable four vortex motion. Phys Fluids 31(10):2796–2801Google Scholar
  244. 244.
    Eckhardt B, Aref H (1988) Integrable and chaotic motions of four vortices. 2. Collision dynamics of vortex pairs. Phil Trans R Soc Lond A 326(1593):655–696Google Scholar
  245. 245.
    Eden C, Böning C (2002) Sources of eddy kinetic energy in the Labrador Sea. J Phys Oceanogr 32(12):3346–3363Google Scholar
  246. 246.
    Eisenlohr H, Eckelmann H (1989) Vortex splitting and its consequences in the vortex street wake of cylinders at low Reynolds number. Phys Fluids A1(2):189–192Google Scholar
  247. 247.
    Elcrat AR, Fornberg B, Horn M, Miller K (2000) Some steady vortex flows past a circular cylinder. J Fluid Mech 409:13–27Google Scholar
  248. 248.
    Elcrat AR, Fornberg B, Miller K (2005) Stability of vortices in equilibrium with a cylinder. J Fluid Mech 544:53–68Google Scholar
  249. 249.
    Elcrat AR, Miller KG (1989) Computation of vortex flows past obstacles with circulation. Phys D 37(1–3):441–452Google Scholar
  250. 250.
    Emelianov M, Claret M, Fraile-Nuez E, Pastor M, Laiz I, Salvador J, Pelegrí JL, Turiel A (2012) Detection of a weak meddy-like anomaly from high-resolution satellite SST maps. In: Espino M, Font J, Pelegrí JL, Sánchez-Arcilla A (eds) Advances in Spanish Physical Oceanography. Sci Mar 76S1:229–234. doi:10.3989/scimar.03619.19IGoogle Scholar
  251. 251.
    Estrade P, Middleton JH (2010) A numerical study of island wake generated by an elliptical tidal flow. Cont Shelf Res 30(9):1120–1135Google Scholar
  252. 252.
    Fang F, Morrow R (2003) Evolution, movement and decay of warm-core Leeuwin Current eddies. Deep Sea Res Part II 50(12–13):2245–2261Google Scholar
  253. 253.
    Fedorov KN (ed) (1986) Intrathermocline eddies in the ocean. PP. Shirshov Institute of Oceanology, Moscow 142 pp (in Russian)Google Scholar
  254. 254.
    Fedorov KN (1986) Intrathermocline eddies—a specific type of oceanic eddies with a core. In: Intrathermocline eddies in the ocean. P.P. Shirshov Institute of Oceanology, Moscow, pp 5–7 (in Russian)Google Scholar
  255. 255.
    Fedorov KN, Ginzburg AI (1992) The near-surface layer of the ocean. VSP. III, Utrecht/Tokyo, 259 ppGoogle Scholar
  256. 256.
    Fedorov KN, Ginzburg AI (1989) Mushroom-like currents (vortex dipoles): one of the most widespread forms of stationary coherent motions in the ocean. In: Nihoul JCJ, Jamart BM (eds) Mesoscale/synoptic coherent structures in geophysical turbulence. Elsevier, Amsterdam/Oxford/New York/Tokyo, pp 1–14Google Scholar
  257. 257.
    Filyushkin BN (1989) Investigation of intrathermocline lenses of Mediterranean origin (Cruise 16 of R/V “Vityaz”, June 3–September 16, 1988). Oceanology 29(4):535–536Google Scholar
  258. 258.
    Filyushkin BN, Aleynik DL, Demidov AN, Sarafanov AA, Kozhelupova NG (2007) The peculiarity of the formation and spreading Mediterranean water mass at intermediate depths of the Atlantic Ocean. In: Waters masses of the oceans and sea. MAX Press, Moscow, pp 92–129 (in Russian)Google Scholar
  259. 259.
    Filyushkin BN, Aleynik DL, Gruzinov VM, Kozhelupova NG (2002) The thermohaline water structure at the region dynamic degradation of the Mediterranean lenses. In: Proceeding of the State Oceanographic Institution, “Ocean and sea research”, S-Ptb. No 208, pp 15–32 (in Russian)Google Scholar
  260. 260.
    Filyushkin BN, Aleynik DL, Gruzinov VM, Kozhelupova NG (2002) Dynamic degradation of the Mediterranean lenses in the Atlantic Ocean. Dokl Earth Sci 387A(9):1079–1082Google Scholar
  261. 261.
    Filyushkin BN, Aleynik DL, Kozhelupova NG, Moshonkin SN (2009) Horizontal transport peculiarities of the Mediterranean water in the Atlantic. In: Komchatov VF (ed) Proceeding of the State Oceanographic Institution, “Ocean and sea research”, vol 212. Moscow, 76–88 (In Russian)Google Scholar
  262. 262.
    Filyushkin BN, Plakhin EA (1995) Experimental study of the first stage of Mediterranean water lens formation. Oceanology 35:797–804Google Scholar
  263. 263.
    Filyushkin BN, Sokolovskiy MA (2011) Modeling the evolution of intrathermocline lenses in the Atlantic Ocean. J Mar Res 69(2–3):191–220Google Scholar
  264. 264.
    Filyushkin BN, Sokolovskiy MA, Kozhelupova NG, Vagina IM (2010) Dynamics of intrathermocline lenses. Dokl Earth Sci 434(part 2):1377–1380Google Scholar
  265. 265.
    Filyushkin BN, Sokolovskiy MA, Kozhelupova NG, Vagina IM (2011) Reflection of intrathermocline eddies on the ocean surface. Dokl Earth Sci 439(part 1):986–989Google Scholar
  266. 266.
    Filyushkin BN, Sokolovskiy MA, Kozhelupova NG, Vagina IM (2011) Evolution of intrathermocline eddies moving over a submarine hill. Dokl Earth Sci 441(part 2):1757–1760Google Scholar
  267. 267.
    Fine KS, Driscoll CF, Molmberg JH, Mitchell TB (1991) Measurements of symmetric vortex merger. Phys Rev Lett 67(5):588–591Google Scholar
  268. 268.
    Finnigan TD, Luther DL, Lukas R (2002) Observations of enhanced diapycnal mixing near the Hawaiian Ridge. J Phys Oceanogr 32(11):2988–3002Google Scholar
  269. 269.
    Fjortoft R (1950) Application of integral theorems in deriving criteria of stability for laminar flows and for the baroclinic circular vortex. Geophys Publ 17(6):1–52Google Scholar
  270. 270.
    Flament P, Lumpkin R, Tourmadre J, Armi L (2001) Vortex pairing in an unstable anticyclonic shear flow: discrete subharmonics of one pendulum day. J Fluid Mech 440:401–409Google Scholar
  271. 271.
    Flatau M, Schubert WH, Stovens DE (1994) The role of baroclinic processes in tropical cyclone motion: the influence of vertical tilt. J Atmos Sci 51(1):2589–2601Google Scholar
  272. 272.
    Flierl GR (1978) Models of vertical structure and the calibration of two-layer models. Dyn Atmos Oceans 2(4):341–381Google Scholar
  273. 273.
    Flierl GR (1987) Isolated eddy models in geophysics. Annu Rev Fluid Mech 19:493–530Google Scholar
  274. 274.
    Flierl GR (1988) On the instability of geostrophic vortices. J Fluid Mech 197:349–388Google Scholar
  275. 275.
    Flierl GR, Carton X, Messager C (1999) Vortex formation by unstable oceanic jets. Eur Ser Appl Ind Math 7:137–150Google Scholar
  276. 276.
    Flierl GR, Larichev VD, McWilliams JC, Reznik GM (1980) The dynamics of baroclinic and barotropic solitary eddies. Dyn Atmos Oceans 5(1):1–41Google Scholar
  277. 277.
    Flierl GR, Stern ME, Whitehead JA Jr (1983) The physical significance of modons: laboratory experiments and general integral constraints. Dyn Atmos Oceans 7(4):233–264Google Scholar
  278. 278.
    Flór J-B, Govers WSS, van Heijst GJF, van Sluis R (1993) Formation of a tripolar vortex in a stratified fluid. Appl Sci Res 51(1–2):405–409Google Scholar
  279. 279.
    Flór J-B, van Heijst GJF (1994) An experimental study of dipolar vortex structures in a stratified fluid. J Fluid Mech 279:101–133Google Scholar
  280. 280.
    Flór JB, van Heijst GJF (1996) Stable and unstable monopolar vortices in a stratified fluid. J Fluid Mech 311:257–287Google Scholar
  281. 281.
    Flór J-B, Hopfinger EJ, Guyez E (2010) Contribution of coherent vortices such as Langmuir cells to wind-driven surface layer mixing. J Geophys Res 115:C10031. doi:10.1029/2009JC005900Google Scholar
  282. 282.
    Freymuth P, Bank W, Palmer M (1984) First experimental evidence of vortex splitting. Phys Fluids 27(5):1045–1046Google Scholar
  283. 283.
    Freymuth P, Bank W, Palmer M (1985) Futher experimental evidence of vortex splitting. J Fluid Mech 152:289–299Google Scholar
  284. 284.
    Freeland HJ, Rhines P, Rossby HT (1975) Statistical observations of trajectories of neutrally buoyant floats in the North Atlantic. J Mar Res 33:383–404Google Scholar
  285. 285.
    Friedrich KO (1953) Special topics in fluid dynamics. New York University Press, New YorkGoogle Scholar
  286. 286.
    Fujiwhara S (1921) The mutual tendency towards symmetry of motion and its application as a principle in meteorology. Q J R Meteorol Soc 47(200):287–293Google Scholar
  287. 287.
    Fujiwhara S (1923) On the growth and decay of vortical systems. Q J R Meteorol Soc 49(206):75–104Google Scholar
  288. 288.
    Fujiwhara S (1931) Short note on the behavior of two vortices. Proc Phys Math Soc Jpn III Ser 13:106–110Google Scholar
  289. 289.
    Fukumoto Y (2003) The three-dimensional instability of a strained vortex tube revisited. J Fluid Mech 493:287–318Google Scholar
  290. 290.
    Gallaire F, Chomaz J-M (2003) Three-dimensional instability of isolated vortices. Phys Fluids 15(8):2113–2126Google Scholar
  291. 291.
    Garrett C, MacCready P, Rhines P (1993) Boundary mixing and arrested Ekman layers: rotating stratified flow near a sloping boundary. Annu Rev Fluid Mech 25:291–323Google Scholar
  292. 292.
    Garrett C, Munk W (1972) Oceanic mixing by breaking internal waves. Deep-Sea Res 19(12):823–832Google Scholar
  293. 293.
    Gent P, McWilliams J (1986) The instability of barotropic circular vortices. Geophys Astrophys Fluid Dyn 35(1–4):209–233Google Scholar
  294. 294.
    Gent P, McWilliams J (1990) Isopycnal mixing in ocean circulation models. J Phys Oceanogr 20(1):150–155Google Scholar
  295. 295.
    Gill AE (1982) Atmosphere-ocean dynamics. Academic, London, 662 ppGoogle Scholar
  296. 296.
    Ginzburg AI, Kostianoy AG, Soloviev DM, Stanichny SV (2000) Remotely sensed coastal/deep-basin water exchange processes in the Black Sea surface. In: Halpern D (ed) Satellite, oceanography and society,  Chapter 15. Elsevier, Amsterdam/Lausanne/New York/Oxford/Shannon/Singapore/Tokyo, pp 273–287
  297. 297.
    Ginzburg AI, Kostianoy AG, Nezlin NP, Soloviev DM, Stanichny SV (2002) Anticyclonic eddies in the northwestern Black Sea. J Mar Syst 32(1–3):91–106Google Scholar
  298. 298.
    Gledzer AE (1999) Mass entrainment and release in ocean eddy structures. Izv Atmos Ocean Phys 35(6):759–766Google Scholar
  299. 299.
    Gluhovsky AB, Klyatskin VI (1977) On dynamics of flipover phenomena in simple hydrodynamic models. Dokl Earth Sci Sec 237:18–20Google Scholar
  300. 300.
    Goldshtik M, Hussain F (1998) Analysis of inviscid vortex breakdown in a semi-infinite pipe. Fluid Dyn Res 23(4):189–234Google Scholar
  301. 301.
    Goncharov VP, Gryanik VM, Pavlov VI (2002) Venusian ‘hot spots’: physical phenomenon and its quantification. Phys Rev E66. doi:10.1103/PhysRevE.66.066304Google Scholar
  302. 302.
    Goncharov VP, Pavlov VI (2001) Cyclostrophic vortices in polar regions of rotating planets. Nonlinear Process Geophys 8(4/5):301–311Google Scholar
  303. 303.
    Goncharov VP, Pavlov VI (2003) Hamitonian contour dynamics. In: Borisov AV, Mamaev IS, Sokolovskiy MA (eds) Fundamental and applied problems of the vortex theory. Institute of Computer Science, Moscow–Izhevsk, pp 179–237 (in Russian)Google Scholar
  304. 304.
    Goncharov VP, Pavlov VI (2008) Hamitonian vortex and wave dynamics. GEOS, Moscow, 432 pp (in Russian)Google Scholar
  305. 305.
    Goosse H, Deleersnijder E, Fichefet T, England MH (1999) Sensitivity of a global coupled ocean-sea ice model to the parameterization of verical mixing. J Geophys Res 104(C6):13681–13685Google Scholar
  306. 306.
    Grant ALM, Belcher SE (2011) Wind-driven mixing below the oceanic mixed layer. J Phys Oceanogr 41(8):1556–1575Google Scholar
  307. 307.
    Greenslade MD, Haynes PH (2008) Vertical transition in transport and mixing in baroclinic flows. J Atmos Sci 65(4):1137–1157Google Scholar
  308. 308.
    Greenspan HP (1990) The theory of rotating fluids. Breukelen Press, Brookline, 352 ppGoogle Scholar
  309. 309.
    Griffiths RW, Hopfinger EJ (1986) Experiments with baroclinic vortex pairs in a rotating fluid. J Fluid Mech 173:501–518Google Scholar
  310. 310.
    Griffiths RW, Hopfinger EJ (1987) Coalescing of geostrophic vortices. J Fluid Mech 178:73–97Google Scholar
  311. 311.
    Griffiths RW, Linden PF (1981) The stability of vortices in a rotating, stratified fluid. J Fluid Mech 105:283–316Google Scholar
  312. 312.
    Griffiths RW, Linden PF (1985) Intermittent baroclinic instability and fluctuations in geophysical circulations. Nature 316(6031):801–803Google Scholar
  313. 313.
    Griffiths RW, Pearce AF (1985) Instability and eddy pairs on the Leeuwin Current south of Australia. Deep-Sea Res 32:1511–1534Google Scholar
  314. 314.
    Grimshaw R, Tanga Y, Broutman D (1994) The effect of vortex stretching on the evolution of barotropic eddies over a topographic slope. Geophys Astrophys Fluid Dyn 76(1–4):43–71Google Scholar
  315. 315.
    Gryanik VM (1983) Dynamics of singular geostrophic vortices in a two-level model of atmosphere (ocean). Izv Atmos Ocean Phys 19(3):171–179Google Scholar
  316. 316.
    Gryanik VM (1983) Dynamics of localized vortex perturbations “vortex charges” in a baroclinic fluid. Izv Atmos Ocean Phys 19(5):347–352Google Scholar
  317. 317.
    Gryanik VM (1988) Localized vortices—“vortex charges” and “vortex filaments” in a baroclinic differentially rotating fluid. Izv Atmos Ocean Phys 24(12):919–926Google Scholar
  318. 318.
    Gryanik VM (1990) About theoretical models of the localized quasi-geostrophic eddies in the atmosphere and ocean. In: Nikiforov EG, Romanov VF (eds) The investigations of vortex dynamics and energetics of the atmosphere, and the problems of climate. Gydrometeoizdat, Leningrad, pp 31–60 (in Russian)Google Scholar
  319. 319.
    Gryanik VM (1991) Dynamics of singular geostrophic vortices near critical points of currents in a N–layer model of the atmosphere (ocean). Izv Atmos Ocean Phys 27:517–526Google Scholar
  320. 320.
    Gryanik VM (1992) Radiation of Rossby waves and adaptation of potential vorticity fields in the atmosphere (ocean). (Dokl) Trans RAS Earth Sci Sect 326(1):976–979Google Scholar
  321. 321.
    Gryanik VM, Borth H, Olbers D (2001) The theory of quasigeostrophic von Kármán vortex streets in two-layer fluids on beta-plane and intermittent turbulent jets. Alfred-Wegener-Institut für Polar- und Meeresforschung, Preprint 106, 59 ppGoogle Scholar
  322. 322.
    Gryanik VM, Borth H, Olbers D (2004) The theory of quasigeostrophic von Kármán vortex streets in two-layer fluids on beta-plane. J Fluid Mech 505:23–57Google Scholar
  323. 323.
    Gryanik VM, Doronina TN (1990) Advective transport of a conservative solute by baroclinic singular quasigeostrophic vortices in the atmosphere (ocean). Izv Atmos Ocean Phys 26(10):1011–1026Google Scholar
  324. 324.
    Gryanik VM, Doronina TN, Olbers D, Warncke TH (2000) The theory of three-dimensional hetons and vortex-dominated spreading in localized turbulent convection in a fast rotating stratified fluid. J Fluid Mech 423:71–125Google Scholar
  325. 325.
    Gryanik VM, Sokolovskiy MA, Verron J (2003) Dynamics of barocline vortices with zero total intensity (hetons). In: Borisov AV, Mamaev IS, Sokolovskiy MA (eds) Fundamental and applied problems of the vortex theory. Institute of Computer Science, Moscow–Izhevsk, pp 547–622 (in Russian)Google Scholar
  326. 326.
    Gryanik VM, Sokolovskiy MA, Verron J (2006) Dynamics of heton-like vortices. Regul Chaotic Dyn 11(3):417–438Google Scholar
  327. 327.
    Gryanik VM, Tevs MV (1989) Dynamics of singular geostrophic vortices in an N-layer model of atmosphere (ocean). Izv Atmos Ocean Phys 25(3):179–188Google Scholar
  328. 328.
    Gryanik VM, Tevs MV (1991) Dynamics of singular geostrophic vortices near critical points of currents in a N-layer model of the atmosphere (ocean). Izv Atmos Ocean Phys 27(7):517–526Google Scholar
  329. 329.
    Gryanik VM, Tevs MV (1997) Dynamics and energetics of heton interacting in linearly and exponentially stratifed media. Izv Atmos Ocean Phys 33(4):385–398Google Scholar
  330. 330.
    Gudimenko AI (2007) Dynamics of perturbed equilateral and collinear configurations of three point vortices. Russ Sci J Nonlinear Dyn 3(4):379–391 (in Russian)Google Scholar
  331. 331.
    Gudimenko AI (2008) Dynamics of perturbed singular confguration of three point vortices. Russ Sci J Nonlinear Dyn 4(2):429–441 (in Russian)Google Scholar
  332. 332.
    Gudimenko AI (2008) Dynamics of perturbed equilateral and collinear configurations of three point vortices. Regul Chaot Dyn 13(2):85–95Google Scholar
  333. 333.
    Gudimenko AI, Zakharenko AD (2010) Qualitative analysis of relative motion of three vortices. Russ Sci J Nonlinear Dyn 6(2):307–326 (in Russian)Google Scholar
  334. 334.
    Gurulev AYu, Kozlov VF (1988) Numerical modeling of structure changes on a potential vorticity front. Izv Atmos Ocean Phys 34(3):395–403Google Scholar
  335. 335.
    Haidvogel DB, Beckmann A, Chapman DC, Lin R-Q (1993) Numerical simulation of flow around a tall isolated seamount. Part II. Resonant generation of trapped waves. J Phys Oceanogr 23(11):2373–2391Google Scholar
  336. 336.
    Hairer E, Nørsett SR, Wanner G (2008) Solving ordinary differential equations. I: Nonstiff Problems. Springer, Berlin, 528 ppGoogle Scholar
  337. 337.
    Hakim GJ, Snyder C, Muraki DJ (2002) A new surface model for cyclone-anticyclone asymmetry. J Atmos Sci 59(16):2405–2420Google Scholar
  338. 338.
    Hart JE, Adler B, Leben R (1988) Cyclonic/anticyclonic gyre asymmetries: laboratory and intermediate-model experiments. Dyn Atmos Oceans 27(1–4):219–232Google Scholar
  339. 339.
    Harvey BJ, Ambaum MHP, Carton XJ (2011) Instability of shielded surface temperature vortices. J Atmos Sci 68(5):964–971Google Scholar
  340. 340.
    Hattori Y, Fukumoto Y (2003) Short-wavelength stability analysis of thin vortex rings. Phys Fluids 15(10):3151–3163Google Scholar
  341. 341.
    Hebert D, Oakey N, Ruddick B (1990) Evolution of a Mediterranean salt lens: scalar properties. J Phys Oceanogr 20(9):1468–1483Google Scholar
  342. 342.
    Helfrich KR, Battisti TM (1991) Experiments on baroclinic vortex shelding from hydrothermal plumes. J Geophys Res 96(C12):12511–12518Google Scholar
  343. 343.
    Helfrich KR, Send U (1988) Finite-amplitude evolution of two-layer geostrophic vortices. J Fluid Mech 197:331–348Google Scholar
  344. 344.
    Hénon A (1976) Family of periodic solutions of the planar three-body problem and their stability. Celest Mech Dyn Astron 13:267–285Google Scholar
  345. 345.
    Herbette S, Morel Y, Arhan M (2003) Erosion of a surface vortex by a seamount. J Phys Oceanogr 33(8):1664–1679Google Scholar
  346. 346.
    Herbette S, Morel Y, Arhan M (2005) Erosion of a surface vortex by a seamount on the β plane. J Phys Oceanogr 35(11):2012–2030Google Scholar
  347. 347.
    Hesthaven JS, Lynov JP, Rasmussen JJ, Sutyrin GG (1993) Generation of tripolar vortical structures on the beta plane. Phys Fluids A5(7):1674–1678Google Scholar
  348. 348.
    Hogan PJ, Hubert HE (2006) Why do intrathermocline eddies form in the Japan/East Sea? A modeling perspective. Oceanography 19(3):134–143Google Scholar
  349. 349.
    Hogg NG (1973) On the stratifed Taylor column. J Fluid Mech 58:517–537Google Scholar
  350. 350.
    Hogg NG, Stommel HM (1985) The heton, an elementary interaction between discrete baroclinic geostrophic vortices, and its implications concerning eddy heat-flow. Proc R Soc Lond A 397:1–20Google Scholar
  351. 351.
    Hogg NG, Stommel HM (1985) Hetonic explosions: the breakup and spread of warm pools as explained by baroclinic point vortices. J Atmos Sci 42(14):1465–1476Google Scholar
  352. 352.
    Hogg NG, Stommel HM (1990) How currents in the upper thermocline could advect meddies deeper down. Deep Sea Res 37(4):613–623Google Scholar
  353. 353.
    Holland GJ, Dietachmayer GS (1993) On the interaction of tropical-cyclone-scale vortices: 3. Continuous barotropic vortices. Q J R Meteorol Soc 119(514):1381–1398Google Scholar
  354. 354.
    Holland GJ, Lander M (1993) The meandering nature of tropical cyclone tracks. J Atmos Sci 50(9):1254–1266Google Scholar
  355. 355.
    Holloway G (1986) Eddies, waves, circulation, and mixing: Statistical geofluid mechanics. Ann Rev Fluid Mech 18:91–147Google Scholar
  356. 356.
    Holmboe J (1968) Instability of baroclinic three-layer models of the atmosphere, vol 27. Geofys Publ Universitetsforlaget, Oslo, pp 1–27Google Scholar
  357. 357.
    Hopfinger EJ, van Heijst GJF (1993) Vortices in rotating fluids. Annu Rev Fluid Mech 25:241–289Google Scholar
  358. 358.
    Horton W, Liu J, Meiss JD, Sedlak JE (1986) Solitary vortices in a rotating plasma. Phys Fluids 29(4):1004–1010Google Scholar
  359. 359.
    Houghton RW, Olson DJ, Celone PJ (1986) Observation of an anticyclonic eddy near the continental shelf break south of New England. J Phys Oceanogr 16(1):60–71Google Scholar
  360. 360.
    Huang RX (1987) A three-layer model for wind-driven circulation in a subtropical-subpolar basin. Part I: Model formulation and the subcritical state; Part 2: The supercritical and hypercritical state. J Phys Oceanogr 17(5):664–678; 679–687Google Scholar
  361. 361.
    Huang RX (1988) A three-layer model for wind-driven circulation in a subtropical-subpolar basin. Part 3: Potential vorticity analisys. J Phys Oceanogr 18(5):739–752Google Scholar
  362. 362.
    Huang RX, Bryan K (1987) A multilayer model of the thermohaline and wind-driven ocean circulation. J Phys Oceanogr 17(11):1909–1924Google Scholar
  363. 363.
    Huang RX, Flierl GR (1987) Two-layer models for the thermocline and current structure in subtropical/subpolar gyres. J Phys Oceanogr 17(6):872–884Google Scholar
  364. 364.
    Huppert HE (1975) Some remarks on the initiation of in-ertial Taylor columns. J Fluid Mech 67:397–412Google Scholar
  365. 365.
    Huppert HE, Bryan K (1976) Topographically generated eddies. Deep Sea Res 23(8):655–679Google Scholar
  366. 366.
    Huq P, Britter RE (1995) Turbulence evolution and mixing in a two-layer stably stratified fluid. J Fluid Mech 285:41–67Google Scholar
  367. 367.
    Husain HS, Shtern V, Hussain F (2003) Control of vortex breakdown by addition of near-axis swirl. Phys Fluids 15(2):271–279Google Scholar
  368. 368.
    Hyun KH, Hogan PJ (2008) Topographic effects on the anticyclonic vortex evolution: a modeling study. Cont Shelf Res 28(10–11):1246–1260Google Scholar
  369. 369.
    Hyun KH, Hogan PJ (2008) Topographic effects on the path and evolution of Loop Current Eddies. J Geophys Res 113(C12). doi:10.1029/2007JC004155Google Scholar
  370. 370.
    Ibraev RA, Kuksa VI, Skirta AYu (2000) Modeling of the passive admixture transfer by the eddy currents in the eastern part of the Black Sea. Oceanology 40(1):18–25Google Scholar
  371. 371.
    Ikeda M (1981) Meanders and detached eddies of a strong easrward-flowing jet using a two-layer quasi-geostrophic model. J Phys Oceanogr 11(4):526–540Google Scholar
  372. 372.
    Ikeda M (1981) Instability and splitting of mesoscale rings using a two-layer quasi-geostrophic model on an f-plane. J Phys Oceanogr 11(7):987–998Google Scholar
  373. 373.
    Ikeda M (1983) Linear instability of a current flowing along a bottom sloping using a three-layer model. J Phys Oceanogr 13(2):208–223Google Scholar
  374. 374.
    Ikeda M, Apel JR (1981) Mesoscale eddies detached from spatially growing meanders in a eastward-flowing oceanic jet using a two-layer quasi-geostrophic model. J Phys Oceanogr 11(12):1638–1661Google Scholar
  375. 375.
    Ingersoll AP (1969) Inertial Taylor columns and Jupiter’s Great Red Spot. J Atmos Sci 26(7):744–752Google Scholar
  376. 376.
    Inoue R, Smyth WD (2009) Efficiency of mixing forced by unsteady shear flow. J Phys Oceanogr 39(5):1150–1166Google Scholar
  377. 377.
    Ishizu M, Kitade Y, Michida Y (2013) Mixing process on the northeast coast of Hokkaido in summer. J Oceanogr 69(1):1–13Google Scholar
  378. 378.
    Ivanov AYu, Ginzburg AI (2002) Oceanic eddies in synthetic aperture radar images. Earth Planet Sci 111(3):281–295Google Scholar
  379. 379.
    Ivanov YuA, Kort VG, Shapovalov SM, Sherbinin AD (1988) Meso-scale intrusion lenses. In: Kort VG (ed) Proceedings hydrophysical studies at “Mesopolygon” program. Nauka, Moscow, pp 41–46 (in Russian)Google Scholar
  380. 380.
    Izrailsky YuG, Koshel KV, Stepanov DV (2008) Determination of optimal excitation frequency range in background flows. Chaos 18(1):013107. doi:10.1063/1.2835349Google Scholar
  381. 381.
    Izrailsky YuG, Kozlov VF, Koshel KV (2003) Some features of chaotization of a pulsating barotropic flow over a seamount with elliptic cross-section. Russ J Numer Anal Math Model 18(3):243–260Google Scholar
  382. 382.
    Izrailsky YuG, Kozlov VF, Koshel KV (2004) Some specific features of chaotization of the pulsating barotropic flow over elliptic and axisymmetric sea-mounts. Phys Fluids 16(8):3173–3190Google Scholar
  383. 383.
    Jacob JP, Chassignet EP, Dewar WK (2002) Influence of topography on the propagation of isolated eddies. J Phys Oceanogr 32(10):2848–2869Google Scholar
  384. 384.
    Jamaloodeen MI, Newton PK (2007) Two-layer quasigeostrophic potential vorticity model. J Math Phys. doi:10.1063/1.2469221Google Scholar
  385. 385.
    Janowitz GS (1975) The effect of bottom topography on stratified flow in the beta-plane. J Geophys Res 80(30):4163–4168Google Scholar
  386. 386.
    Jeong J, Hussain F (1995) On the identification of a vortex. J Fluid Mech 285:69–94Google Scholar
  387. 387.
    Jiménez J (1975) Stability of a pair of co-rotating vortices. Phys Fluids 18(11):1580–1581Google Scholar
  388. 388.
    Jiménez J, Wray AA (1998) On the characteristics of vortex filaments in isotropic turbulence. J Fluid Mech 371:255–285Google Scholar
  389. 389.
    Johnson ER (1977) Stratified Taylor columns on a beta-plane. Geophys Astrophys Fluid Dyn 9(1):159–177Google Scholar
  390. 390.
    Johnson ER (1978) Trapped vortices in rotating flow. J Fluid Mech 86(2):209–224Google Scholar
  391. 391.
    Johnson ER (1978) Topographically bound vortices. Geophys Astrophys Fluid Dyn 11(1):61–71Google Scholar
  392. 392.
    Johnson ER (1979) Finite depth stratified flow over topography on a beta-plane. Geophys Astrophys Fluid Dyn 12(1):35–43Google Scholar
  393. 393.
    Johnson J, Ambar I, Serra N, Stevens I (2002) Comparative studies of the spreading of Mediterranean water through the Culf Cadiz. Deep-Sea Res II 49:4179–4193Google Scholar
  394. 394.
    Jones C, Winkler S (2002) Invariant manifolds and Lagrangian dynamics in the ocean and atmosphere. In: B Hasselblatt, B Fiedler, AB Katok (eds) Handbook of dynamical systems, vol 2,  Chap. 2. Elsevier, Amsterdam/New York/North Holland, pp 55–29
  395. 395.
    Jones H, Marshall J (1993) Convection with rotation in a neutral ocean: a study of deep-ocean convection. J Phys Oceanogr 23(6):1009–1039Google Scholar
  396. 396.
    Josserand Ch, Rossi M (2007) The merging of two co-rotating vortices: a numerical study. Eur J Mech B/Fluids 26(6):779–794Google Scholar
  397. 397.
    Junglaus JH (1999) A three-dimensional simulation of the formation of anticyclonic lenses (meddies) by the instability of an intermediate depth boundary current. J Phys Oceanogr 29(6):1579–1598Google Scholar
  398. 398.
    Juza M, Penduff T, Brankart J-M, Barnier B (2012) Estimating the distortion of mixed layer porperty distributions by the ARGO sampling. J Oper Oceanogr 5(1):45–58Google Scholar
  399. 399.
    Kalashnik MV, Svirkunov PN (1996) Symmetric stability of the cyclostrophic and geostrophic balance states in a stratified medium. (Dokl) Trans RAS/Earth Sci Sec 349(5):829–831Google Scholar
  400. 400.
    Kalashnik MV, Svirkunov PN (1996) Cyclostrophic and geostrophic lalance states in a shallow-water model. Izv Atmos Ocean Phys 32(3):370–377Google Scholar
  401. 401.
    Kalashnik MV, Visheratin KN (2008) Cyclostrophic adjustment in swirling gas flows and the Ranque-Hilsch vortex tube effect. J Exp Theor Phys 106(4):819–829Google Scholar
  402. 402.
    Kalashnik MV, Visheratin KN (2010) Cyclostrophic adjustment and nonlinear oscillations in the core of intense atmospheric vortex. Izv Atmos Ocean Phys 46(5):591–596Google Scholar
  403. 403.
    Kamenkovich VM (1977) Fundamentals of ocean dynamics. Elsevies Sci. Publ. Co., Amsterdam/New York 249 ppGoogle Scholar
  404. 404.
    Kamenkovich VM, Koshlyakov MN, Monin AS (1986) Synoptic eddies in the ocean. EFM, D. Reidel Publishing Company, Dordrecht, 433 ppGoogle Scholar
  405. 405.
    Kamenkovich VM, Larichev VD, Khar’kov BV (1982) A numerical barotropic model for analysis of synoptic eddies in the open ocean. Oceanology 21(6):549–558Google Scholar
  406. 406.
    Kapela T, Simó C (2007) Computer assisted proofs for nonsymmetric planar choreographies and for stability of the Eight. Nonlinearity 20(5):1241–1255Google Scholar
  407. 407.
    Kapela T, Zgliczyński P (2003) The existence of simple choreographies for N-body problem—a computer assisted proof. Nonlinearity 16(6):1899–1918Google Scholar
  408. 408.
    Käse RH, Zenk W (1987) Reconstructed Mediterranean salt lens trajectories. J Phys Oceanogr 17(1):158–161Google Scholar
  409. 409.
    Karsten R, Jones H, Marshal J (2002) The role of eddy transfer in setting the stratification and transport of a circumpolar current. J Phys Oceanogr 32(1):39–54Google Scholar
  410. 410.
    Kawakami A, Funakoshi M (1999) Chaos motion of fluid particles around a rotating elliptic vortex in a linear shear flow. Fluid Dyn Res 25(4):167–193Google Scholar
  411. 411.
    Kennelly MA, Evans RH, Joyce TM (1985) Small-scale cyclones on the periphery of Gulf Stream warm-core rings. J Geophys Res 90(C5):8845–8857Google Scholar
  412. 412.
    Kerswell RR (2002) Elliptical instability. Annu Rev Fluid Mech 34:83–113Google Scholar
  413. 413.
    Khvoles R, McWilliams JC, Kizner Z (2007) Non-coincidence of separatrices in two-layer modons. Phys Fluids 19(5):056602. doi:10.1063/1.2731741Google Scholar
  414. 414.
    Kida S (1981) Motion of an elliptic vortex in an uniform shear flow. J Phys Soc Jpn 50(10):3517–3520Google Scholar
  415. 415.
    Killworth PD (1983) On the motion of isolated lenses on a beta-plane. J Phys Oceanogr 13(3):368–376Google Scholar
  416. 416.
    Kirchhoff G (1876) Vorlesungen über mathematische Physik: Mechanik. Taubner, LeipzigGoogle Scholar
  417. 417.
    Kiya M, Takeo H, Mochizuki O, Kudo D (1999) Simulating vortex pairs interacting with mixing-layer vortices. Fluid Dyn Res 24(1):61–79Google Scholar
  418. 418.
    Kizner ZI (1984) Rossby solitons with axially symmetric baroclinic modes. Dokl (Trans) USSR Acad Sci 275:211–214Google Scholar
  419. 419.
    Kizner ZI (1985) Interpretation of soliton solutions to the equation of quasi-geostrophic vorticity in a baroclinic ocean. Izv Atmos Ocean Phys 21:330–332Google Scholar
  420. 420.
    Kizner ZI (1986) Intensity of synoptic eddies and the quasigeostrophic approximation. Oceanology 26(1):16–20Google Scholar
  421. 421.
    Kizner ZI (1986) Strongly nonlinear solitary Rossby waves. Oceanology 26(3):284–289Google Scholar
  422. 422.
    Kizner ZI (1988) On the theory of intrathermocline eddies. Dokl (Trans) USSR Akad Sci 300:213–216Google Scholar
  423. 423.
    Kizner ZI (1997) Solitary Rossby waves with baroclinic modes. J Mar Res 55(4):671–685Google Scholar
  424. 424.
    Kizner Z (2006) Stability and transitions of hetonic quartets and baroclinic modons. Phys Fluids 18(5):056601. doi:10.1063/1.2196094Google Scholar
  425. 425.
    Kizner Z (2008) Hetonic quartet: exploring the transitions in baroclinic modons. In: Borisov AV, Kozlov VV, Mamaev IS, Sokolovskiy MA (eds) IUTAM symposium on Hamiltonian dynamic, vortex strictures, turbulence (IUTAM Bookseries, vol 6). Springer, New York, pp 125–133Google Scholar
  426. 426.
    Kizner Z (2011) Stability of point-vortex multipoles revisited. Phys Fluids 23(6):064104. doi:10.1063/1.3596270Google Scholar
  427. 427.
    Kizner Z, Berson D, Khvoles R (2002) Baroclinic modon equilibria on the beta-plane: stability and transitions. J Fluid Mech 468:239–270Google Scholar
  428. 428.
    Kizner Z, Berson D, Khvoles R (2003) Non-circular baroclinic modons: constructing stationary solutions. J Fluid Mech 489:199–228Google Scholar
  429. 429.
    Kizner Z, Berson D, Reznik G, Sutyrin G (2003) The theory of the beta-plane baroclinic topographic modons. Geophys Astrophys Fluid Dyn 97(3):175–211Google Scholar
  430. 430.
    Kizner Z, Khvoles R (2004) The tripole vortex: experimental evidence and explicit solutions. Phys Rev E 70(1):016307. doi:10.1103/PhysRevE.70.0163072004Google Scholar
  431. 431.
    Kizner Z, Khvoles R (2004) Two variations on the theme of Lamb-Chaplygin: supersmooth dipole and rotating multipoles. Regul Chaotic Dyn 9(4):509–518Google Scholar
  432. 432.
    Kizner Z, Khvoles R, McWilliams JC (2007) Rotating multipoles on the f- and γ-planes. Phys Fluids 19(1):016603. doi:10.1063/1.2432915Google Scholar
  433. 433.
    Kizner Z, Reznik GM, Fridman B, Khvoles R, McWilliams JC (2008) Shallow-water modons on the f-plane. J Fluid Mech 603:305–329Google Scholar
  434. 434.
    Klocker A, Ferrari R, LaCasce JH (2012) Estimating suppression of eddy mixing by mean flows. J Phys Oceanogr 42(9):1566–1576Google Scholar
  435. 435.
    Kloosterziel RC, van Heijst GJF (1989) On tripolar vortices. In: Nihoul JCJ, Jamart BM (eds) Mesoscale/synoptic coherent structures in geophysical turbulence. Elsevier, Amsterdam/Oxford/New York/Tokyo, pp 609–625Google Scholar
  436. 436.
    Kloosterziel RC, van Heijst GJF (1991) An experimental study of unstable barotropic vortices in a rotating fluid. J Fluid Mech 223:1–24Google Scholar
  437. 437.
    Klyatskin VI (2007) Stochastic equations. Theory and its applications in acoustics, hydrodynamics, and radio physics. Fizmatlit, Moscow. V. 1: Basic regulations, exact results, and asymptotic approximations, 318 pp. V. 2: Coherent phenomena in stochastic dynamic systems, 343 pp (in Russian)Google Scholar
  438. 438.
    Kochin NE, Kibel XA, Roze NV (1965) Theoretical hydrodynamics. Wiley, New York, 577 ppGoogle Scholar
  439. 439.
    Koiller J, Carvalho SP, Silva RR, Oliveira LCG (1985) On Aref’s vortex motions with a symmetry center. Phys D 16(1):27–61Google Scholar
  440. 440.
    Koshel KV, Izrail’ski YuG, Stepanov DV (2006) Determining the optimal frequency of perturbation in the problem of chaotic transport of particles. Dokl Phys 51(4):219–222Google Scholar
  441. 441.
    Koshel KV, Prants SV (2006) Chaotic advection in the ocean. Phys Usp (Adv Phys Sci) 49:1151–1178Google Scholar
  442. 442.
    Koshel KV, Prants SV (2008) Chaotic advection in the ocean. Institute of Computer Science, Moscow–Izhevsk, 364 pp (in Russian)Google Scholar
  443. 443.
    Koshel KV, Sokolovskiy MA, Davies PA (2008) Chaotic advection and nonlinear resonances in an oceanic flow above submerged obstacle. Fluid Dyn Res 20(10):695–736Google Scholar
  444. 444.
    Koshel KV, Sokolovskiy MA, Verron J (2013) Three-vortex quasi-geostrophic dynamics in a two-layer fluid. Part 2. Regular and chaotic advection around the perturbed steady states. J Fluid Mech 717:255–280Google Scholar
  445. 445.
    Koshel KV, Stepanov DV (2005) Boundary effect on the mixing and transport of passive impurities in a nonstationary flow. Tech Phys Lett 31(2):135–137Google Scholar
  446. 446.
    Koshel KV, Stepanov DV (2006) Chaotic advection induced by a topographic vortex in baroclinic ocean. Dokl Earth Sci 407(2):455–459Google Scholar
  447. 447.
    Koshlyakov MN, Panteleev GG (1988) Termohaline characteristic of the Mediterranean water lens at tropical zone North Atlantic. In: Kort VG (ed) Proceedings hydrophysical studies at “Mesopolygon” program, Nauka, Moscow, pp 46–57 (in Russian)Google Scholar
  448. 448.
    Koszalka I, Caballos L, Bracco A (2010) Vertical mixing and coherent anticyclones in the ocean: the role of stratification. Nonlinear Process Geophys 17(1):37–47Google Scholar
  449. 449.
    Kozlov VF (1969) Lectures on the theory of stationary ocean currents (study guide for students in oceanography). Far Eastern State University, Vladivostok, 383 pp (in Russian)Google Scholar
  450. 450.
    Kozlov VF (1975) Mutual adaptation of the mass and current fields to the bottom relief in a baroclinic ocean. Izv Atmos Ocean Phys 11(1):23–28Google Scholar
  451. 451.
    Kozlov VF (1977) Geostrophic motion of a stratified fluid above an uneven bottom. Izv Atmos Ocean Phys 13(9):657–662Google Scholar
  452. 452.
    Kozlov VF (1980) Formation of a Rossby wave under the action of diturbances in a nonstationary barotropic oceanic flow. Izv Atmos Ocean Phys 16(4):275–279Google Scholar
  453. 453.
    Kozlov VF (1981) On a stationary problem of topographical cyclogenesis in a rotating fluid. Izv Atmos Ocean Phys 17(11):878–882Google Scholar
  454. 454.
    Kozlov VF (1982) Quasistationary geostrophic motion of weakly stratified fluid in the ocean with arbitrary bottom relief. Izv Atmos Ocean Phys 18(7):574–578Google Scholar
  455. 455.
    Kozlov VF (1983) The method of contour dynamics in model problems of the ocean topographic cyclogenesis. Izv Atmos Ocean Phys 19(8):635–640Google Scholar
  456. 456.
    Kozlov VF (1984) Models of the topographic vortices in ocean. Nauka, Moscow, 200 pp (in Russian)Google Scholar
  457. 457.
    Kozlov VF (1985) Construction of a numerical model of geostrophic eddies in a baroclinic fluid based on the Contour Dynamics Method. Izv Atmos Ocean Phys 21(2):161–163Google Scholar
  458. 458.
    Kozlov VF (1991) Construction of the stationary states of vortex patches by the method of perturbations. Izv Atmos Ocean Phys 27(2):77–86Google Scholar
  459. 459.
    Kozlov VF (1992) Model of two-dimensional vortex motion with an entrainment mechanism. Fluid Dyn 27(6):793–798Google Scholar
  460. 460.
    Kozlov VF (1992) A nonlinear model for Kirchoff vortex dissipation. Oceanology 32(4):427–430Google Scholar
  461. 461.
    Kozlov VF (1993) Model of the interaction of elliptic vortex patches with entrainment effects. Izv Atmos Ocean Phys 29(1):90–96Google Scholar
  462. 462.
    Kozlov VF (1994) Geophysical hydrodynamics of vortical patches. Phys Oceanogr 6(1):25–34Google Scholar
  463. 463.
    Kozlov VF (1995) Background currents in geophysical hydrodynamics. Izv Atmos Ocean Phys 31(2):229–234Google Scholar
  464. 464.
    Kozlov VF, Gurulev AYu (1996) Barotropic eddy evolution near a rectilinear bottom break. Izv Atmos Ocean Phys 32(2):249–256Google Scholar
  465. 465.
    Kozlov VF, Gurulev AYu (1997) Moment model of the dynamics of barotropic vortex over a marine trench (ridge) of rectangular section. Izv Atmos Ocean Phys 33(6):837–844Google Scholar
  466. 466.
    Kozlov VF, Gurulev AYu (1998) Dynamics of the front of potential vorticity in the field of background currents. Izv Atmos Ocean Phys 34(3):395–403Google Scholar
  467. 467.
    Kozlov VF, Koshel KV (1999) Barotropic model of chaotic advection in background flows. Izv Atmos Ocean Phys 31(1):123–130Google Scholar
  468. 468.
    Kozlov VF, Koshel KV (2000) A model of chaotic transport in the barotropic background flow. Izv Atmos Ocean Phys 36(1):109–118Google Scholar
  469. 469.
    Kozlov VF, Koshel KV (2001) Some features of chaos development in an oscillatory barotropic flow over an axisymmetric submerged obstacle. Izv Atmos Ocean Phys 37(3):351–361Google Scholar
  470. 470.
    Kozlov VF, Koshel KV (2003) Chaotic advection in the models for background flows of geophysical hydrodynamics. In: Borisov AV, Mamaev IS, Sokolovskiy MA (eds) Fundamental and applied problems of the vortex theory. Institute of Computer Science, Moscow–Izhevsk, pp 471–504 (in Russian)Google Scholar
  471. 471.
    Kozlov VF, Koshel KV, Stepanov DV (2005) Influence of the boundary on the chaotic advection in the simplest model of a topographic vortex. Izv Atmos Ocean Phys 41(2):217–227Google Scholar
  472. 472.
    Kozlov VF, Makarov VG (1984) Evolution modeling of unstable geostrophic eddies in a barotropic ocean. Oceanology 24(5):556–560Google Scholar
  473. 473.
    Kozlov VF, Makarov VG (1985) Simulation of the instability of axisymmetric vortices using the contour dynamics method. Fluid Dyn 20(1):28–34Google Scholar
  474. 474.
    Kozlov VF, Makarov VG (1995) Background currents in the Sea of Japan (a barotropic model). Oceanology 35(5):601–604Google Scholar
  475. 475.
    Kozlov VF, Makarov VG (1996) Background currents in the Sea of Japan (a two-layer quasi-geostrophicc model). Oceanology 36(4):453–457Google Scholar
  476. 476.
    Kozlov VF, Makarov VG (1996) Background currents in the Sea of Okhotsk. Russ Meteorol Hydrol 1(9):39–44Google Scholar
  477. 477.
    Kozlov VF, Makarov VG, Sokolovskiy MA (1986) Numerical model of the baroclinic instability of axially symmetric eddies in two-layer ocean. Izv Atmos Ocean Phys 22(8):674–678Google Scholar
  478. 478.
    Kozlov VF, Sal’nikov PYu (1989) Mechanism for the formation of mushroom-shaped flows with dense packing of vortices. Izv Atmos Ocean Phys 25(4):324–326Google Scholar
  479. 479.
    Kozlov VF, Sal’nikov PYu (1990) The jet (pulse) model of mushroom-like flow formation. Phys Oceanogr 1(3):171–175Google Scholar
  480. 480.
    Kozlov VF, Shavlyugin AI (1992) Stationary arrays of vortical patches near linear boundaries. Phys Oceanogr 3(4):241–250Google Scholar
  481. 481.
    Kozlov VF, Sokolovskiy MA (1978) Stationary motion of a stratified fluid above a rough bottom (geostrophic approximation on the β–plane). Oceanology 18(4):383–386Google Scholar
  482. 482.
    Kozlov VF, Sokolovskiy MA (1980) Influence of cylindrical topographic disturbanced on a nonstationary zonal flow of a stratified fluid on the beta plane. Izv Atmos Ocean Phys 16(8):596–604Google Scholar
  483. 483.
    Kozlov VF, Sokolovskiy MA (1981) Meander of a barotropic zonal current crossing a bottom ridge (periodic regime). Oceanology 21(6):684–687Google Scholar
  484. 484.
    Kozlov VF, Yaroshchuk EV (1986) Numerical modeling of structural transitions in a plane shear layer. Fluid Dyn 21(5):712–715Google Scholar
  485. 485.
    Kozlov VV (2003) General theory of vortices. Dynamical Systems, X, Encyclopaedia of Mathematical Sciences, vol 67. Springer, BerlinGoogle Scholar
  486. 486.
    Kozlov VV (1996) Symmetries, topology and resonances in Hamiltonian mechanics. Springer, BerlinGoogle Scholar
  487. 487.
    Krasnopolskaya TS, Meleshko VV, Peters GWM, Meijer HEH (1999) Mixing in Stokes flow in an annular wedge cavity. Eur J Mech B/Fluids 18(5):793–822Google Scholar
  488. 488.
    Kuksa VI (1983) The intermediate waters of the World Ocean. Gydrometeoizdat, Leningrad, 272 pp (in Russian)Google Scholar
  489. 489.
    Kulik KN, Tur AV, Yanovsky VV (2010) Interaction of point and dipole vortices in an incompressible liquid. Theor Math Phys 162(3):383–400Google Scholar
  490. 490.
    Kundu PK, Cohen IM, Hu HH (2004) Fluid mechanics. Academic, New York 759 ppGoogle Scholar
  491. 491.
    Kunze E, Sanford T (1993) Submesoscale dynamics near a seamount. Part I: measurements of ertel vorticity. J Phys Oceanogr 23(12):2567–2588Google Scholar
  492. 492.
    Kuo AC, Polvani LM (2000) Nonlinear geostrophic adjustment, cyclone/anticyclone asymmetry, and potential vorticity rearrangement. Phys Fluids 12(5):1087. Google Scholar
  493. 493.
    Kuo H-C, Chen GT-J, Lin C-H (2000) Merger of tropical cyclones Zeb and Alex. Mon Weather Rev 128(8):2967–2975Google Scholar
  494. 494.
    Kuo H-C, Williams RT, Chen GT-J, Chen Y-L (2001) Topographic effects on barotropic vortex motion: no mean flow. J Atmos Sci 58(10):1310–1327Google Scholar
  495. 495.
    Kurakin LG, Yudovich VI (2002) On nonlinear stability of steady rotation of a regular vortex polygon. Dokl Phys 47(6):465–470Google Scholar
  496. 496.
    Kurakin LG, Yudovich VI (2002) The stability of stationary rotation of a regular vortex polygon. Chaos 12(3):574–595Google Scholar
  497. 497.
    Kurganskiy MV (1990) On the motion of a pair of vortices on the beta-plane. In: Nikiforov EG, Romanov VF (eds) The investigations of vortex dynamics and energetics of the atmosphere, and the problems of climate. Gydrometeoizdat, Leningrad, pp 123–130 (in Russian)Google Scholar
  498. 498.
    Kusch HA, Ottino JM (1992) Experiments on mixing in continuous chaotic flows. J Fluid Mech 236:319–348Google Scholar
  499. 499.
    Kuzmina NP, Zhurbas VM, Rudels B, Stipa T, Paka VT, Muraviev SS (2008) Role of eddies and intrusions in the exchange processes in the Baltic halocline. Oceanology 48(2):149–158Google Scholar
  500. 500.
    Kuznetsov L, Zaslavsky GM (1998) Regular and chaotic advection in the flow field of a three-vortex system. Phys Rev E 58(6):7330–7349Google Scholar
  501. 501.
    Kuznetsov L, Zaslavsky GM (2000) Passive particle transport in three-vortex flow. Phys Rev E 61(4):3777–3792Google Scholar
  502. 502.
    Kvaleberg E, Morey SL, O’Brien JJ (2003) Frontogenesis and subsequent formation of cold filaments and eddies on an idealized shelf. Oceans 5:2831–2834Google Scholar
  503. 503.
    LaCasce JH (1998) A geostrophic vortex over a slope. J Phys Oceanogr 28(12):2362–2381Google Scholar
  504. 504.
    Ladyzhenskaya OA (1969) The mathematical theory of viscous incimpressible flow. 2nd Eng. edition revised and enlarged. Gordon and Breach Science Publishers, New York/London/Paris/Mintreux/Tokyo/Melbourne, 224 ppGoogle Scholar
  505. 505.
    Lahaye N, Zeitlin V (2011) Collisions of ageostrophic modons and formation of new types of coherent structures in rotating shallow water model. Phys Fluids 23(6):061703
  506. 506.
    Lahaye N, Zeitlin V (2012) Existence and properties of ageostrophic modons and coherent tripoles in the two-layer rotating shallow water model on the f-plane. J Fluid Mech 706:71–107Google Scholar
  507. 507.
    Lahaye N, Zeitlin V (2012) Shock modon: a new type of coherent structure in rotating shallow water. Phys Rev Lett 108(4):044502. doi:10.1103/PhysRevLett.108.044502Google Scholar
  508. 508.
    Lam JS-L, Dritschel DG (2001) On the beta-drift of an initially circular vortex patch. J Fluid Mech 436:107–129Google Scholar
  509. 509.
    Lamb H (1885) Hydrodynamics, 2nd edn. Cambridge University Press, CambridgeGoogle Scholar
  510. 510.
    Lamb H (1932) Hydrodynamics, 6th edn. Cambridge University Press, CambridgeGoogle Scholar
  511. 511.
    Landau LD, Lifshits EM (1959) Fluid mechanics. Pergamon Press, New York, 536 ppGoogle Scholar
  512. 512.
    Lander MA (1995) The merger of two tropical cyclones. Mon. Weather Rev 123(7):2260–2265Google Scholar
  513. 513.
    Lander M, Holland GJ (1993) On the interaction of tropical-cyclone-scale vortices: 1. Observations. Q J R eteorol Soc 119(514):1347–1361Google Scholar
  514. 514.
    Lansky IM, O’Neil TM, Schecter DA (1997) A theory of vortex merger. Phys Rev Lett 79(8):1479–1482Google Scholar
  515. 515.
    Large WG, McWilliams JC, Doney SC (1994) Oceanic vertical mixing: a review and a model with a nonlocal boundary layer parametrization. Rev Geophys 32:363–403Google Scholar
  516. 516.
    Larichev VD, Reznik GM (1976) Two-dimensional solitary Rossby waves. Dokl Akad Nauk SSSR 231(5):1077–1079Google Scholar
  517. 517.
    Larichev VD, Reznik GM (1976) Strongly nonlinear, two-dimensional solitary Rossby waves. Oceanology 16(6):547–550Google Scholar
  518. 518.
    Larichev VD, Reznik GM (1982) Numerical experiments on the study of collision of two-dimensional solitary Rossby waves. Dokl Akad Nauk SSSR 264:229–233Google Scholar
  519. 519.
    Larichev VD, Reznik GM (1983) On collisions between two-dimensional solitary Rossby waves. Oceanology 23(5):545–552Google Scholar
  520. 520.
    Laurent LSt, Naveira Garabato AC, Ledwell JR, Thurnherr AM, Toole JM, Watson AJ (2012) Turbulence and diapycnal mixing in Drake Passage. J Phys Oceanogr 42(12):2143–2152Google Scholar
  521. 521.
    Lavrova OYu, Kostyanoy AG, Lebedev SA, Mityagina VI, Ginzburg AI, Sheremet NA (2011) Complex satellite monitoring of the Russian seas. Space Research Institute of RAS, Moscow, 470 ppGoogle Scholar
  522. 522.
    Lazutkin VF (1990) Analytic integrals of a semistandard mapping, and separatrix splitting. Leningr Math J 1(2):427–445Google Scholar
  523. 523.
    Le Dizés S, Verga A (2002) Viscous interactions of two co-rotating vortices before merging. J Fluid Mech 467:389–410Google Scholar
  524. 524.
    Legg S (2004) A simple criterion to determine the transition from a localized convection to a distributed convection regime. J Phys Oceanogr 34(12):2843–2846Google Scholar
  525. 525.
    Legg S, Jones H, Visbeck M (1996) A heton perspective of baroclinic eddy transfer in localized open ocean convection. J Phys Oceanogr 26(10):2251–2266Google Scholar
  526. 526.
    Legg S, Marshall J (1993) A heton model of the spreading phase of open-ocean deep convection. J Phys Oceanogr 23(6):1040–1056Google Scholar
  527. 527.
    Legg S, Marshall J (1998) The influence of the ambient flow on the spreading of convected water masses. J Mar Res 56(1):107–139Google Scholar
  528. 528.
    Legg S, McWilliams J, Gao J (1998) Localization of deep ocean convection by a mesoscale eddy. J Phys Oceanogr 28(5):944–970Google Scholar
  529. 529.
    Legras B, Dritschel DG (1991) The elliptical model of two-dimensional vortex dynamics. I. The basic state. Phys Fluids A3(5):845–854Google Scholar
  530. 530.
    Legras B, Dritschel DG (1993) A comparison of the contour surgery and pseudo-spectral method. J Comput Phys 104(2):287–302Google Scholar
  531. 531.
    Leibovich S, Stewartson K (1983) A sufficient condition for the instability of columnar vortices. J Fluid Mech 126:335–356Google Scholar
  532. 532.
    Leith CE (1984) Minimum enstrophy vortices. Phys Fluids 27(6):1388–1395Google Scholar
  533. 533.
    Lenn Y-D, Rippeth TP, Old CP, Bacon S, Polyakov I, Ivanov V, Hölemann J (2011) Intermittent intense turbulent mixing under ice in the Laptev Sea continental shelf. J Phys Oceanogr 41(3):531–547Google Scholar
  534. 534.
    Leoncini X, Kuznetsov L, Zaslavsky GM (2000) Motion of three vortices near collapse. Phys Fluids 12(8):1911–1927Google Scholar
  535. 535.
    Leoncini X, Kuznetsov L, Zaslavsky GM (2001) Chaotic advection near a three-vortex collapse. Phys Rev E 63(3):036224. doi:10.1103/PhysRevE.63.036224Google Scholar
  536. 536.
    Leoncini X, Zaslavsky GM (2002) Jets, stickiness, and anomalous transport. Phys Rev E 65(4):046216. doi:10.1103/PhysRevE.65.046216Google Scholar
  537. 537.
    Levina GV, Montgomery MT (2010) A first examination of the helical nature of tropical cyclogenesis. Dokl Earth Sci 434(part 1):1285–1289Google Scholar
  538. 538.
    Li M, Trowbridge J, Geyer R (2008) Asymmetric tidal mixing due to the horizontal density gradient. J Phys Oceanogr 38(2):418–434Google Scholar
  539. 539.
    Liang X, Thurnherr AM (2012) Eddy-modulated internal waves and mixing on a midocean ridge. J Phys Oceanogr 42(7), 1242–1248Google Scholar
  540. 540.
    Lim CC, Majda AJ (2001) Point vortex dynamics for coupled surface/interior QG and propagating heton clasters in models for ocean convection. Geophys Astrophys Fluid Dyn 94(3–4):177–220Google Scholar
  541. 541.
    Lim CC, Nebus J (2007) Vorticity, statistics, and Monte Carlo simulation. Springer, New York, 290 pp (Springer monographs in mathematics)Google Scholar
  542. 542.
    Lin S-J (1992) Contour dynamics of tornado-like vortices. J Atmos Sci 49(18):1745–1756Google Scholar
  543. 543.
    Liu C, Köhl A, Stammer D (2012) Adjoint-based estimation of eddy-induced tracer mixing parameters in the global ocean. J Phys Oceanogr 42(7):1186–1206Google Scholar
  544. 544.
    Love AEH (1893) On the stability of certain vortex motion. Proc Lond Math Soc s1–25:18–43Google Scholar
  545. 545.
    Love AEH (1893) On the motion of paired vortices with a common axis. Proc Lond Math Soc s1–25:185–194Google Scholar
  546. 546.
    Lovegrove AF, Moroz IM, Read PL (2001) Bifurcation and instabilities in rotating two-layer fluids: 1. f-plane. Nonlinear Process Geophys 8(1):21–36Google Scholar
  547. 547.
    Lovegrove AF, Moroz IM, Read PL (2002) Bifurcation and instabilities in rotating, two-layer fluids: 2. β-plane. Nonlinear Process Geophys 9(3–4):289–309Google Scholar
  548. 548.
    Lugt HJ (1996) Introduction to vortex theory. Vortex Flow Press. Potomac 627 ppGoogle Scholar
  549. 549.
    Lumpkin R, Flament P, Kloosterziel R, Armi L (2000) Vortex merging in a \(1\frac{1} {2}\)-layer fluid on an f-plane. J Phys Oceanogr 30(1):233–242Google Scholar
  550. 550.
    Luzzatto-Fegiz P, Williamson CHK (2010) Stability of elliptical vortices from “Imperfect–Velocity–Impulse” diagrams. Theor Comput Fluid Dyn 24(1–4):181–188Google Scholar
  551. 551.
    Luzzatto-Fegiz P, Williamson CHK (2010) Stability of conservative flows and new steady-fluid solutions from bifurcation diagrams exploiting a variational argument. Phys Rev Lett 104:044504. doi:10.1103/PhysRevLett.104.044504Google Scholar
  552. 552.
    Luzzatto-Fegiz P, Williamson CHK (2011) An efficient and general numerical method to compute steady uniform vortices. J Comput Phys 230(17):6495–6511Google Scholar
  553. 553.
    Luzzatto-Fegiz P, Williamson CHK (2012) Determining the stability of steady two-dimensional flows through imperfect velocity-impulse diagrams. J Fluid Mech 706:323–350Google Scholar
  554. 554.
    Luzzatto-Fegiz P, Williamson CHK (2012) Structure and stability of the finite-area von Kármán street. Phys Fluids 24(6):066602. Google Scholar
  555. 555.
    Maas LRM, Zahariev K (1996) An exact, stratified model of a meddy. Dyn Atmos Oceans 24:215–225Google Scholar
  556. 556.
    Madelain F (1970) Influence de la topographie du fond sur l’écoulement Méditerranéen entre le Détroit de Gibralter et le cap Saint-Vincent. Cah Oceanogr 22:43–61Google Scholar
  557. 557.
    Makarov VG (1990) A program code for investigation of plane vortex currents in an ideal fluid by the method of contour dynamics. In: Kozlov VF (ed) Method of contour dynamics in oceanological investigations. FED USSR Acad Sci, Vladivostok, pp 28–39 (in Russian)Google Scholar
  558. 558.
    Makarov VG (1991) Computational algorithm of the contour dynamics method with changeable topology of domains under study. Model Mekh 5(4):83–95Google Scholar
  559. 559.
    Makarov VG (1996) Numerical simulation of the formation of tripolar vortices by the method of contour dynamics. Izv Atmos Ocean Phys 32(1):40–49Google Scholar
  560. 560.
    Makarov VG, Bulgakov SN (2008) Regimes of near-wall vortex dynamics in potential flow through gaps. Phys Fluids 20(12):086605. doi:10.1063/1.2969471Google Scholar
  561. 561.
    Makarov VG, Kizner Z (2011) Stability and evolution of uniform-vorticity dipoles. J Fluid Mech 672:307–325Google Scholar
  562. 562.
    Makarov VG, Sokolovskiy MA, Kizner Z (2012) Doubly symmetric finite-core heton equilibria. J Fluid Mech 708:397–417Google Scholar
  563. 563.
    Mallik DD (1979) Influence of bottom topography on the zonal geostrophic flow in a stratified-ocean model. Izv Atmos Ocean Phys 15(10):781–783Google Scholar
  564. 564.
    Malikova NP, Permyakov MS (2010) Effect of the Ekman boundary layer on the evolution of vortex formations. Fluid Dyn 45(6):905–908Google Scholar
  565. 565.
    Malvern LE (1969) Introduction to the mechanics of continous medium. Englewood Cliffs, Prentice-Hall, 713 ppGoogle Scholar
  566. 566.
    Mancho AM, Small D, Wiggins S (2006) A tutorial on dynamical systems concepts applied to Lagrangian transport in oceanic flows defined as finite time data sets: theoretical and computational issues. Phys Rep 437(3–4):55–124Google Scholar
  567. 567.
    Mao X, Sherwin ST, Blackburn HM (2012) Non-normal dynamics of time-evolving co-rotating vortex pairs. J Fluid Mech 701:430–459Google Scholar
  568. 568.
    Mariotti A, Legras B, Dritschel DG (1994) Vortex stripping and the erosion of coherent structures in two-dimensional flows. Phys Fluids 6(12):3954–3962Google Scholar
  569. 569.
    Marshall JS (1995) Chaotic oscillations and breakup of quasigeostrophic vortices in the N-layer approximation. Phys Fluids 7(5):983–992Google Scholar
  570. 570.
    Marshall JS, Parthasarathy B (1993) Tearing of an aligned vortex by a current difference in two-layer quasi-geostrophic flow. J Fluid Mech 225:157–182Google Scholar
  571. 571.
    Marshall J, Schott F (1999) Open-ocean convection: observation, theory, and models. Rev Geophys 37(1):1–64Google Scholar
  572. 572.
    Martinsen-Burrell N, Julien K, Patersen MR, Weiss JB (2006) Merger and alignment in a reduced model for three-dimensional quasigeostrophic ellipsoidal vortices. Phys Fluids 18(5):057101. doi:10.1063/1.21918872006Google Scholar
  573. 573.
    Masina S, Pinardi N (1993) The halting effect of baroclinicity in vortex merging. J Phys Oceanogr 23(8):1618–1637Google Scholar
  574. 574.
    Matsuura T (1980) On a decay process if isolated, intense vortices in a two-layer ocean. J Oceanogr Soc Jpn 36(1):39–45Google Scholar
  575. 575.
    Matsuura T (1995) The evolution of frontal-geostrophic vortices in two-layer ocean. J Phys Oceanogr 25(10):2298–2318Google Scholar
  576. 576.
    Maxworthy T, Narimousa S (1994) Unsteady, turbulent convection into a homogeneous rotating fluid, with oceanographic applications. J Phys Oceanogr 24(5):865–887Google Scholar
  577. 577.
    Mazé JP, Arhan M, Mercier H (1997) Volume budget of the eastern boundary layer off the Iberian Peninsula. Deep-Sea Res I 44(9–10):1543–1574Google Scholar
  578. 578.
    McDonald NR (1998) The motion of an intense vortex near topography. J Fluid Mech 367:359–377Google Scholar
  579. 579.
    McDonald NR (2000) The interaction of two baroclinic geostrophic vortices on the β-plane. Proc R Lond A 456:1029–1049Google Scholar
  580. 580.
    McDonald NR (2004) A new translating quasigeostrophic V-state. Eur J Mech B/Fluids 23(4):633–644Google Scholar
  581. 581.
    McWilliams JC (1983) Interaction of isolated vortices. II: Modon generation by monopole collision. Geophys Astrophys Fluid Dyn 24(1):1–22Google Scholar
  582. 582.
    McWilliams JC (1985) Submesoscale, coherent vortices in the ocean. Rev Geophys 23(2):165–182Google Scholar
  583. 583.
    McWilliams JC (1996) Modeling the oceanic general circulation. Annu Rev Fluid Mech 28:215–248Google Scholar
  584. 584.
    McWilliams JC (2006) Fundamentals of geophysical fluid dynamics. Cambridge University Press, Cambridge, 266 ppGoogle Scholar
  585. 585.
    McWilliams JC, Flierl GR, Larichev VD, Reznik GM (1981) Numerical studies of barotropic modons. Dyn Atmos Oceans 5(4):219–238Google Scholar
  586. 586.
    McWilliams JC, Zabusky N (1982) Interaction of isolated vortices. I: Modons colliding with modons. Geophys Astrophys Fluid Dyn 19(3–4):207–227Google Scholar
  587. 587.
    Meacham SP (1991) Meander evolution on piecewise-uniform, quasi-geostrophic jets. J Phys Oceanogr 21(8):1139–1170Google Scholar
  588. 588.
    Meacham SP, Pankratov KK, Shchepetkin AF, Zhmur VV (1994) The interaction of ellipsoidal vortices with background shear flows in a stratified fluid. Dyn Atmos Oceans 21(2–3):167–212Google Scholar
  589. 589.
    Melander MV, McWilliams JC, Zabusky NJ (1987) Asymmetrization and vorticity-gradient intensification of an isolated two-dimensional vortex through filamentation. J Fluid Mech 178:137–159Google Scholar
  590. 590.
    Melander MV, Zabusky NJ, McWilliams JC (1987) Asymmetric vortex merger in two dimensions: which vortex is ‘victorious’? Phys Fluids 30(9):2610–2612Google Scholar
  591. 591.
    Melander MV, Zabusky NJ, McWilliams JC (1988) Symmetric vortex merger in two dimensions: causes and conditions. J Fluid Mech 195:303–340Google Scholar
  592. 592.
    Melander MV, Zabusky NJ, Styczek AS (1986) A moment model for vortex interactions of the two-dimensional Euler equations. Part 1. Computational validation of a Hamiltonian elliptical representation. J Fluid Mech 167:95–115Google Scholar
  593. 593.
    Meleshko VV, Aref H (2007) A bibliography of vortex dynamics 1858–1956. Adv Appl Mech 41:197–292Google Scholar
  594. 594.
    Meleshko VV, Galaktionov OS, Peters GWM, Meijer HEH (1999) Three-dimensional mixing in Stokes flow: the partitioned pipe mixer problem revisited. Eur J Mech B/Fluids 18(5):783–792Google Scholar
  595. 595.
    Meleshko VV, Konstantinov MYu (1993) Dynamics of vortex structures. Kiev Naukova Dumka 280 pp (in Russian)Google Scholar
  596. 596.
    Meleshko VV, Konstantinov MYu, Gurzhi AA, Konovaljuk TP (1992) Advection of a vortex pair atmosphere in a velocity field of point vortices. Phys Fluids A 4(12):2779–2797Google Scholar
  597. 597.
    Meleshko VV, van Heijst GJF (1994) Interaction of two-dimensional vortex structures: point vortices, contour kinematics and stirring properties. Chaos Solitons Fract 4(6):977–1010Google Scholar
  598. 598.
    Meleshko VV, van Heijst GJF (1994) On Chaplygin’s investigations of two-dimensional vortex structures in an inviscid fluid. J Fluid Mech 272:157–182Google Scholar
  599. 599.
    Mellor GL (1996) Introduction to physical oceanography. Springer, New York, 260 ppGoogle Scholar
  600. 600.
    Meschanov SL, Shapiro GI (1998) A young lens of Red Sea water in Arabian Sea. Deep-Sea Res Part I 45(1):1–13Google Scholar
  601. 601.
    Mesquita SB, Prahalad YS (1999) Statistical stationary states for a two-layer quasi-geostrophic system. Proc Indian Acad Sci (Math Sci) 109(1):107–115Google Scholar
  602. 602.
    Meunier P, Ehrenstein U, Leweke T, Rossi M (2002) A merger criterion for two-dimensional co-rotating vortices. Phys Fluids 14(8):2757–2766Google Scholar
  603. 603.
    Meunier P, Leweke T (2001) Three-dimensional instability during vortex merging. Phys Fluids 13(10):2747–2751Google Scholar
  604. 604.
    Meunier P, Leweke T (2005) Elliptic instability of a co-rotating vortex pair. J Fluid Mech 533:125–159Google Scholar
  605. 605.
    Middleton JH (2009) Topographic eddies. In: Steele JH, Thorpe SA, Turekian KK (eds) Ocean currents. Elsevier, New York, pp 462–469Google Scholar
  606. 606.
    Mied RP, Lindemann GJ (1982) The birth and evolution of eastward-propagating modons. J Phys Oceanogr 12(3):213–230Google Scholar
  607. 607.
    Mied RP, McWilliams JC, Lindemann GJ (1991) The generation and evolution of mushroom-like vortices. J Phys Oceanogr 21(4):489–510Google Scholar
  608. 608.
    Mikhailovskii AB, Kudashev VR, Lakhin VP, Mikhailovskaya LA, Smolyakov AI, Shishkov SYu (1984) Chains of Rossby solitons and gradient solitons. JETP Lett 40(7):1054–1056Google Scholar
  609. 609.
    Miller PD, Pratt LJ, Helfrich KR, Jones CKRT (2002) Chaotic transport of mass and potential vorticity for an island recirculation. J Phys Oceanogr 32(1):80–102Google Scholar
  610. 610.
    Milne-Thomson LM (1962) Theoretical hydrodynamics, 4th edn. London: MacMillan & co.Google Scholar
  611. 611.
    Mindlin IM (1984) On vorticity-induced waves in a homogeneous incompressible fluid. J Appl Math Mech 48(5):550–555Google Scholar
  612. 612.
    Minobe S, Kanamoto Y, Okada N, Ozawa H, Ikeda M (2000) Plume structures in deep convection of rotating fluid. J Jpn Soc Fluid Mech 19(6):395–396Google Scholar
  613. 613.
    Mirabel AP, Monin AS (1988) Instability of ocean circulation patterns. Trans Dokl USSR Acad Sci Earth Sci Sect 303(6):253–256Google Scholar
  614. 614.
    Mirabel AP, Monin AS (1989) Instability of gyres in a continuously startified ocean. Trans Dokl USSR Acad Sci Earth Sci Sect 309(6):267–270Google Scholar
  615. 615.
    Mitchell TB, Rossi LF (2008) The evolution of Kirchhoff elliptic vortices. Phys Fluids 20:054103. doi:10.1063/1.291299120Google Scholar
  616. 616.
    Miyama T, McCreary JP Jr, Jensen TG, Loschnigg J, Godfrey S, Ishida A (2003) Structure and dynamics of the Indian-Ocean cross-equatorial cell. Deep Sea Res Part II 50(12–13):2023–2047Google Scholar
  617. 617.
    Miyazaki T (1992) Elliptical instability in a stably stratified rotating fluid. Phys Fluids A 5(11):2702–2709Google Scholar
  618. 618.
    Miyazaki T, Fukumoto Y (1992) Three-dimensional instability of strained vortices in a stably stratified fluid. Phys Fluids A 4(11):2515–2522Google Scholar
  619. 619.
    Miyazaki T, Imai T, Fukumoto Y (1995) Three-dimensional instability of Kirchhoff’s elliptic vortex. Phys Fluids 7(1):195–202Google Scholar
  620. 620.
    Mizuta R, Yoden S (2001) Chaotic mixing and transport barriers in an idealized stratospheric polar vortex. J Atmos Sci 58(17):2616–2629Google Scholar
  621. 621.
    Mokhov II, Doronina TN, Gryanik VM, Khairullin RR, Korovkina LV, Lagun VE, Mokhov OI, Naumov EP, Petukhov VK, Senatorsky AO, Tevs MV (1994) Extratropical cyclones and anticyclones: tendencies of change. In: Gronas S, Shapiro MA (eds) The life of extratropical cyclones, vol 2. Geophysical Institute, University of Bergen, Bergen, pp 56–60Google Scholar
  622. 622.
    Mokhov II, Gryanik VM, Doronina TN, Lagun DE, Mokhov OI, Naumov EP, Petukhov VK, Tevs MV, Khairullin RR (1993) Vortex activity in the atmosphere: tendencies of changes. Moscow: Institute of Atmospheric Physics of RAS, Preprint N 2, 97 ppGoogle Scholar
  623. 623.
    Möller JD, Montgomery MT (2000) Tropical cyclone evolution via potential vorticity anomalies in a three-dimensional balance model. J Atmos Sci 57(20):3366–3387Google Scholar
  624. 624.
    Monin AS (1990) Theoretical geophysical fluid dynamics. Kluwer Academic Publishers, Dordrecht, 429 ppGoogle Scholar
  625. 625.
    Monin AS, Yaglom AM (1971) Statistical fluid mechanics, vols I and II. MIT Press, CambridgeGoogle Scholar
  626. 626.
    Monin AS, Zhikharev GM (1990) Ocean eddies. Sov Phys Usp 33(5):313–339Google Scholar
  627. 627.
    Moore C (1993) Braids in classical dynamics. Phys Rev Lett 70(24):3675–3679Google Scholar
  628. 628.
    Moore DV, Saffman PG (1975) The density of organized vortices in a turbulent mixing layer. J Fluid Mech 69(3):465–473Google Scholar
  629. 629.
    Moore DW, Saffman PG, Tanveer S (1988) The calculation of some Batchelor flows: the Sadovskii vortex and rotational corner flow. Phys Fluids 31(5):978–990Google Scholar
  630. 630.
    Morel YG (1995) The influence of an upper thermocline current on intrathermocline eddies. J Phys Oceanogr 25(12):3247–3252Google Scholar
  631. 631.
    Morel YG, Carton XJ (1994) Multipolar vortices in two-dimensional incompressible flows. J Fluid Mech 267:23–51Google Scholar
  632. 632.
    Morel YG, McWilliams J (1997) Evolution of isolated interior vortices in the ocean. J Phys Oceanogr 27(5):727–748Google Scholar
  633. 633.
    Morel YG, McWilliams J (2001) Effect of isopycnal and diapycnal mixing on the stability of oceanic currents. J Phys Oceanogr 31(8):2280–2296Google Scholar
  634. 634.
    Morikawa GK (1960) Geostrophic vortex motion. J Meteorol 17(6):148–158Google Scholar
  635. 635.
    Morikawa GK, Swenson EV (1971) Interacting motion of rectilinear geostrophic vortices. Phys Fluids 14(6):1058–1073Google Scholar
  636. 636.
    Nakamura N (2008) Sensitivity of global mixing and fluxes to isolated transport barriers. J Atmos Sci 65(12):3800–3818Google Scholar
  637. 637.
    Narimousa S, Maxworthy T (1985) Two-layer model of shear-driven coastal upwelling in the presence of bottom topography. J Fluid Mech 159:503–531Google Scholar
  638. 638.
    Nauw JJ, Dijkstra HA, Simonnet E (2004) Regimes of low-frequency variability in a three-layer quasi-geostrophic ocean model. J Mar Res 62(5):685–720Google Scholar
  639. 639.
    Negretti ME, Billant P (2013) Stability of a Gaussian pancake vortex in a stratified fluid. J Fluid Mech 718:457–480Google Scholar
  640. 640.
    Newton PK (2001) The N-vortex problem: analytical techniques. Applied Mathematical Sciences, vol 145. Springer, New York/Berlin/Heidelberg, 421 ppGoogle Scholar
  641. 641.
    Newton PK, Ross SD (2006) Chaotic advection in the restricted four-vortex problem on a sphere. Phys D 223:36–53Google Scholar
  642. 642.
    Nezlin MV (1986) Rossby solitons (Experimental investigations and laboratory model of natural vortices of the Jovian Great Red Spot type). Sov Phys Usp 29(9):807–842Google Scholar
  643. 643.
    Nezlin MV, Rylov AYu, Trubnikov AS, Khutoretski AV (1990) Cyclonic-anticyclonic asymmetry and a new soliton concept for rossby vortices in the laboratory, oceans and the atmospheres of giant planets. Geophys Astrophys Fluid Dyn 52(41):211–247Google Scholar
  644. 644.
    Nezlin MV, Sutyrin GG (1994) Problems of simulation of large, long-lived vortices in the atmospheres of the giant planets (Jupiter, Saturn, Neptune). Surv Geophys 15(1):63–99Google Scholar
  645. 645.
    Ngan K, Shepherd TG (1997) Chaotic mixing and transport in Rossby-wave critical layer. J Fluid Mech 334:315–351Google Scholar
  646. 646.
    Ngan K, Shepherd TG (1999) A closer look at chaotic advection in the stratosphere. Part I: Geometric structure. J Atmos Sci 56(24):4134–4152Google Scholar
  647. 647.
    Ngan K, Shepherd TG (1999) A closer look at chaotic advection in the stratosphere. Part II: Statistical diagnostics. J Atmos Sci 56(24):4153–4166Google Scholar
  648. 648.
    Nikitin OP (1997) Vertical structure of synoptic currents in the northeast tropical Pacific. Oceanology 37(6):737–748Google Scholar
  649. 649.
    Nof D (1983) The translation of isolated cold eddies on a sloping bottom. Deep-Sea Res 30(2A):171–182Google Scholar
  650. 650.
    Nof D (1991) Lenses generated by intermittent currents. Deep-Sea Res 38(3):325–345Google Scholar
  651. 651.
    Nof D (1993) Generation of ringlets. Tellus 45A(4):299–310Google Scholar
  652. 652.
    Nof D, Simon LM (1987) Laboratory experiments on the merging of nonlinear anticyclonic eddies. J Phys Oceanogr 17(3):343–357Google Scholar
  653. 653.
    Norbury J (1975) Steady planar vortex pairs in an ideal fluid. Commun Pure Appl Maths 38:697–700Google Scholar
  654. 654.
    Novikov EA (1975) Dynamics and statistics of a system of vortices. Sov Phys JETP 41(5):937–943Google Scholar
  655. 655.
    Novikov EA, Sedov YuB (1978) Stochastic properties of a four-vortex system. Sov Phys JETP 48:440–444Google Scholar
  656. 656.
    Novikov EA, Sedov YuB (1979) Stochastization of vortices. JETP Lett 29(12):677–679Google Scholar
  657. 657.
    Nycander J (1987) Propagation of discontinuities in the Hasegawa-Mima equation. Phys Fluids 30(6):1585–1587Google Scholar
  658. 658.
    Nycander J (1988) New stationary vortex solutions of the Hasegawa-Mima equation. J Plasma Phys 39(3):413–430Google Scholar
  659. 659.
    Nycander J (1992) Refutation of stability proofs for dipole vortices. Phys Fluids A 4(3):467–476Google Scholar
  660. 660.
    Nycander J (1994) Steady vortices in plasmas and geophysical flows. Chaos 4(2):253–268Google Scholar
  661. 661.
    Nycander J (1995) Existence and stability of stationary vortices in a uniform shear flow. J Fluid Mech 287:193–132Google Scholar
  662. 662.
    Nycander J, Döös K, Coward AC (2002) Chaotic and regular trajectories in the Antarctic Circumpolar Current. Tellus 54A(1):99–106Google Scholar
  663. 663.
    Nycander J, Lacasce JH (2004) Stable and unstable vortices attached to seamounts. J Fluid Mech 507:71–94Google Scholar
  664. 664.
    Nycander J, Pavlenko VP (1987) Global vortex pattern in a rotating plasma. Phys Fluids 30(7):2097–2100; 507:71–94Google Scholar
  665. 665.
    Nycander J, Pavlenko VP (1991) Stationary propagating magnetic electron vortices. Phys Fluids B 3(6):1386–1391Google Scholar
  666. 666.
    Oey L-Y (1988) A model of Gulf Stream frontal instabilities, meanders and eddies along the continental slope. J Phys Oceanogr 18(2):211–229Google Scholar
  667. 667.
    Okamoto A, Hara K, Nagaoka K, Yoshimura S, Vranješ J, Kono M, Tanaka MY (2003) Experimental observation of a tripolar vortex in a plasma. Phys Plasmas 10(6):2211. Google Scholar
  668. 668.
    Olbers D, Wolff JO, Volker C (2000) Eddy fluxes and second-order moment balances for non-homogeneous quasigeostrophic turbulence in wind-driven zonal flows. J Phys Oceanogr 30(7):1645–1668Google Scholar
  669. 669.
    Oliver KIC, Eldevik T, Stevens DP, Watson AJ (2008) A Greenland See perspective on the dynamics of postconvective eddies. J Phys Oceanogr 38(12):2755–2771Google Scholar
  670. 670.
    Olson DB (1991) Rings in the Ocean. Ann Rev Earth Planet Sci 19:283–311Google Scholar
  671. 671.
    Olson DB, Brown OB, Emmerson SR (1983) Gulf Stream statistics from Florida Straits to Cape Hatteras derived from satellite and historical data. J Geophys Res 88(C8):4569–4577Google Scholar
  672. 672.
    Olson DB, Schmitt RW, Kennelly MA, Joyce TM (1985) A two-layer diagnostic model of a long-time physical evolution of warm-core ring 82 B. J Geophys Res 90(C5):8813–8822Google Scholar
  673. 673.
    Onsager L (1949) Statistical hydrodynamics. Il Nuovo Cim (1943–1954) 6(2):279–287Google Scholar
  674. 674.
    Orlandi P (1990) Vortex dipole rebound from a wall. Phys Fluids 2(A8):1429–1436Google Scholar
  675. 675.
    Orlandi P, van Heijst GF (1992) Numerical simulation of tripolar vortices in 2D flow. Fluid Dyn Res 9(4):179–206Google Scholar
  676. 676.
    Ottino JM (1989) The kinematics of mixing: Stretching, chaos and transport. Cambridge University Press, Cambridge, 362 ppGoogle Scholar
  677. 677.
    Ottino JM (1990) Mixing, chaotic advection, and turbulence. Annu Rev Fluid Mech 22:207–253Google Scholar
  678. 678.
    Ottino JM, Khakhar DV (2000) Mixing and segregation of rganular. Annu Rev Fluid Mech 32:55–91Google Scholar
  679. 679.
    Overman EA II (1986) Steady-state solutions of the Euler equations in two dimensions. II. Local analysis of limiting V-states. SIAM J Appl Math 46(5):765–800Google Scholar
  680. 680.
    Overman EA II, Zabusky NJ (1982) Evolution and merger of isolated vortex structures. Phys Fluids 25(8):1297–1305Google Scholar
  681. 681.
    Paillet J, Le Cann B, Carton X, Morel Y, Serpette A (2002) Dynamics and evolution of a northern meddy. J Phys Oceanogr 32(1):55–79Google Scholar
  682. 682.
    Paillet J, Le Cann B, Serpette A, Morel Y, Carton X (1999) Real-time tracking of a Galician meddy. Geophys Res Lett 26(13):1877–1880Google Scholar
  683. 683.
    Paldor N, Boss E (1994) Chaotic trajectories of tidally perturbed internal oscillations. J Atmos Sci 49(23):2306–2318Google Scholar
  684. 684.
    Paldor N, Nof D (1990) Linear instability of an anticyclonic vortex in a two-layer ocean. J Geophys Res 95(C10):18075–18079Google Scholar
  685. 685.
    Pallás-Sauz E, Viúdez Á (2008) Spontaneous generation of inertia-gravity waves during the merging of two baroclinic anticyclones. J Phys Oceanogr 38(1):213–234Google Scholar
  686. 686.
    Pavia EG, Cushman-Roisin B (1990) Merging of frontal eddies. J Phys Oceanogr 20(12):1886–1906Google Scholar
  687. 687.
    Pavlenko VP, Petviashvili VI (1983) Solitary vortex in a flute instability. Sov J Plasma Phys 9:603–604Google Scholar
  688. 688.
    Pedlosky J (1985) The instability of continuous heton clouds. J Atmos Sci 42(14):1477–1486Google Scholar
  689. 689.
    Pedlosky J (1987) Geophysical fluid dynamics. Springer, New York, 710 ppGoogle Scholar
  690. 690.
    Pedlosky J (1996) Ocean circulation theory. Springer, New York, 453 ppGoogle Scholar
  691. 691.
    Perepelkin VV, Petrov AG (1983) Dynamics of an elliptic vortex. Fluid Dyn 18(4):539–544Google Scholar
  692. 692.
    Perrot X, Carton X (2009) Point-vortex interaction in an oscillatory deformation field: Hamiltonian dynamics, harmonic resonance and transition to chaos. Discret Contin Dyn Syst Ser B 11(4):971–995Google Scholar
  693. 693.
    Peters D, Vargin P, Körnich H (2007) A study of the zonally asymmetric tropospheric forcing of the austral vortex splitting during September 2002. Tellus 59A(3):384–394Google Scholar
  694. 694.
    Pierce RB, Fairlie TDA (1993) Chaotic advection in the stratosphere: implications for the dispersal of chemically perturbed air from the polar vortex. J Geophys Res 98(D10):18589–18596Google Scholar
  695. 695.
    Pierce RB, Fairlie TD, Grose WL, Swinbank R, O’Neil A (1994) Mixing processes within the polar night jet. J Atmos Sci 51(20):2957–2972Google Scholar
  696. 696.
    Pierrehumbert RT (1980) A family of steady, translating vortex pairs with distributed vorticity. J Fluid Mech 99:129–144Google Scholar
  697. 697.
    Pierrehumbert RT (1991) Large-scale horizontal mixing in planetary atmospheres. Phys Fluids A 3(5):1250–1260Google Scholar
  698. 698.
    Pierrehumbert RT (1991) Chaotic mixing of tracer and vorticity by modulated travelling Rossby waves. Geophys Astrophys Fluid Dyn 58(1–4):285–319Google Scholar
  699. 699.
    Pierrehumbert RT, Yang H (1993) Global chaotic mixing on isentropic surfaces. J Atmos Sci 50(15):2462–2480Google Scholar
  700. 700.
    Płotka H, Dritschel DG (2012) Quasi-geostrophic shallow-water vortex-patch equilibria and their stability. Geophys Asrophys Fluid Dyn 106(6):574–595Google Scholar
  701. 701.
    Płotka H, Dritschel DG (2013) Quasi-geostrophic shallow-water doubly-connected vortex equilibria and their stability. J Fluid Mech 723:40–68Google Scholar
  702. 702.
    Poincaré H (1893) Théorie des tourbillons. Gauthier-Villars, ParisGoogle Scholar
  703. 703.
    Poje AC, Haller G (1999) Geometry of cross-stream mixing in a double-gyre ocean model. J Phys Oceanogr 29(8):1649–1665Google Scholar
  704. 704.
    Polvani LM (1991) Two-layer geostrophic vortex dynamics. 2. Alignment and two-layer V-states. J Fluid Mech 225:241–270Google Scholar
  705. 705.
    Polvani LM, Carton XJ (1990) The tripole: a new coherent vortex structure of incompressible two-dimensional flows. Geophys Astrophys Fluid Dyn 51(1–4):87–102Google Scholar
  706. 706.
    Polvani LM, Flierl GR (1986) Generalized Kirchhoff vortices. Phys Fluids 29(8):2376–2379Google Scholar
  707. 707.
    Polvani LM, Flierl GR, Zabusky NJ (1989) Filamentation of unstable vortex structures via separatrix crossing: a quantitative estimate of onset time. Phys Fluids A1(2):181–184Google Scholar
  708. 708.
    Polvani LM, Plumb RA (1991) Rossby wave breaking, microbreaking, filamentation, and secondary vortex formation: the dynamics of a perturbed vortex. J Atmos Sci 49(6):462–476Google Scholar
  709. 709.
    Polvani LM, Wisdom J (1990) Chaotic Lagrangian trajectories around an elliptical vortex parch embedded in a constant and uniform background shear flow. Phys Fluids A 2(2):123–126Google Scholar
  710. 710.
    Polvani LM, Zabusky NJ, Flierl GR (1988) Applications of contour dynamics to two-layer quasi-geostrophic flows. Fluid Dyn Res 3(1–4):422–424Google Scholar
  711. 711.
    Polvani LM, Zabusky NJ, Flierl GR (1989) Two-layer geostrophic vortex dynamics: 1. Upper-layer V-states and merger. J Fluid Mech 205:215–242Google Scholar
  712. 712.
    Polzin KL, Toole JM, Ledwell JR, Schmitt RW (1997) Spatial variability of turbulent mixing in the abyssal ocean. Science 276(5309):93–96Google Scholar
  713. 713.
    Pozrikidis C (2008) Numerical computation in science and engineering, 2nd edn. Oxford University Press, New YorkGoogle Scholar
  714. 714.
    Pozrikidis C (2009) Fluid dynamics: theory, computation and numerical simulation, 2nd edn. Springer, LondonGoogle Scholar
  715. 715.
    Pozrikidis C (2011) Introduction to theoretical and computational fluid dynamics, 2nd edn. Cambridge University Press, CambridgeGoogle Scholar
  716. 716.
    Prandtl L (1952) Essentials of fluid dynamics. Blackie and Son, LondonGoogle Scholar
  717. 717.
    Prants SV (2013) Dynamical systems theory methods to study mixing and transport in the ocean. Phys Scr 87(3):038115. doi:10.1088/0031-8949/87/03/038115Google Scholar
  718. 718.
    Prants SV, Budyansky MV, Uleysky MYu, Zaslavsky GM (2006) Chaotic mixing and transport in a meandering jet flow. Chaos 16(3):033117.
  719. 719.
    Prater MD, Sanford TB (1994) A meddy off Cape St. Vincent. Part I: description. J Phys Oceanogr 24(7):1572–1586Google Scholar
  720. 720.
    Pratt LJ (1983) On inertial flow over topography. Part 1. Semigeostrophic adjustment to an obstacle. J Fluid Mech 131:195–218Google Scholar
  721. 721.
    Price JF, O’Neil Baringer M, Lueck RG, Johnson GC, Ambar I, Parrilla G, Cantos A, Kennelly MA, Sanford TB (1993) Mediterranean outflow mixing and dynamics. Science 259(5099):1277–1282Google Scholar
  722. 722.
    Price T (1993) Chaotic scattering of two identical point vortex pairs. Phys Fluids A5(10):2479–2483Google Scholar
  723. 723.
    Prieto R, McNoldy BD, Fulton SR, Schubert WH (2003) A classification of binary tropical cyclone-like vortex interactions. Mon Weather Rev 131(11):2656–2666Google Scholar
  724. 724.
    Prudnikov AP, Brychkov YA, Marichev OI (1986) Integrals and series, vol. 1: elementary functions. Gordon and Breach, New YorkGoogle Scholar
  725. 725.
    Prudnikov AP, Brychkov YA, Marichev OI (1990) Integrals and series, vol. 2: special functions. Gordon and Breach, New YorkGoogle Scholar
  726. 726.
    Pullin DL (1992) Contour dynamics methods. Annu Rev Fluid Mech 24:89–115Google Scholar
  727. 727.
    Rabinovich AB (1997) Spectral analysis of tsunami waves: separation of source and topography effects. J Geophys Res 102(C6):12663–12676Google Scholar
  728. 728.
    Radko T (2008) Long-range interaction and elastic collisions of isolated vortices. J Fluid Mech 610:285–310Google Scholar
  729. 729.
    Raymond DJ, Jiang H (1990) A theory of long-living mesoscale convective system. J Atmos Sci 47(24):3067–3077Google Scholar
  730. 730.
    Reinaud JN, Carton X (2009) The stability and the nonlinear evolution of quasi-geostrophic hetons. J Fluid Mech 636:109–135Google Scholar
  731. 731.
    Reinaud JN, Dritschel DG (2002) The merger of vertically offset quasi-geostrophic vortices. J Fluid Mech 469:287–315Google Scholar
  732. 732.
    Reinaud JN, Dritschel DG (2005) The critical merger distance between two co-rotating quasi-geostrophic vortices. J Fluid Mech 522:357–381Google Scholar
  733. 733.
    Reinaud JN, Dritschel DG, Koudella CR (2003) The shape of vortices in quasi-geostrophic turbulence. J Fluid Mech 474:175–192Google Scholar
  734. 734.
    Reznik GM (1987) Synoptic movements above a strongly dissected bottom relief. Trans Dokl USSR Acad Sci Earth Sci Sect 296(5):230–233Google Scholar
  735. 735.
    Reznik GM (1999) On the generation of subsurface motions over a sloping bottom in a two-layer ocean. Oceanology 39(3):293–295Google Scholar
  736. 736.
    Reznik GM, Grimshaw RHJ, Sriskanderejan K (1997) On basic mechanisms governing two-layer vortices on a beta-plane. Geophys Astrophys Fluid Dyn 86(1–4):1–42Google Scholar
  737. 737.
    Reznik GM, Kizner Z (2007) Two-layer quasi-geostrophic singular vortices embedded in a regular flow: 1. Invariants of motion and stability of vortex pairs. J Fluid Mech 584:185–202Google Scholar
  738. 738.
    Reznik GM, Kizner Z (2007) Two-layer quasi-geostrophic singular vortices embedded in a regular flow: 2. Steady and unsteady drift of individual vortices on a beta plane. J Fluid Mech 584:203–223Google Scholar
  739. 739.
    Reznik GM, Sutyrin GG (2001) Baroclinic topographic modons. J Fluid Mech 437:121–142Google Scholar
  740. 740.
    Reznik GM, Tsybaneva TB (1994) On the influence of topography and stratification on planetary waves in the ocean (two-layer model). Oceanology 34(1):1–9Google Scholar
  741. 741.
    Reznik GM, Tsybaneva TB (1999) Planetary waves in a stratified ocean of variable depth. Part 1. Two-layer model. J Fluid Mech 388:115–145Google Scholar
  742. 742.
    Reznik GM, Zeitlin V, Ben Jellool M (2001) Nonlinear theory of geostrophic adjustment. Part 1. Rotating shallow-water model. J Fluid Mech 445:93–120Google Scholar
  743. 743.
    Rhines PB (1986) Vorticity dynamics of the oceanic general circulation. Annu Rev Fluid Mech 18:433–497Google Scholar
  744. 744.
    Ricca RL (ed) (2001) An introduction to the geometry and topology of fluid flows. NATO ASI Series II, 47. Kluwer, Dordrecht/Boston/LondonGoogle Scholar
  745. 745.
    Ricca RL (ed) (2009) Lectures on topological fluid mechanics. Springer-CIME Lecture Notes in Mathematics 1973. Springer, HeidelbergGoogle Scholar
  746. 746.
    Riccardi G (2004) Motion of an elliptical uniform vortex outside a circular cylinder. Regul Chaotic Dyn 9(4):399–415Google Scholar
  747. 747.
    Riccardi G, Piva R, Benzi R (1995) A physical model for merging in two-dimensional decaying turbulence. Phys Fluids 7(12):3091–3103Google Scholar
  748. 748.
    Richardson PL, Bower AS, Zenk W (1999) Summary of meddies tracked by floats. Int WOCE Newsl 34:18–20Google Scholar
  749. 749.
    Richardson PL, Bower AS, Zenk W (2000) A census of meddies tracked by floats. Progr Oceanogr 45(2):209–250Google Scholar
  750. 750.
    Richardson PL, Maillard C, Sanford TB (1979) The physical structure and life history of cyclonic Gulf Stream ring Allen. J Geophys Res 84(C12):7727–7741Google Scholar
  751. 751.
    Richardson PL, Tychensky A (1998) Meddy trajectories in the Canary Basin measured during the SEMAPHORE experiment 1993–1995. J Geophys Res 103(C11):25029–25045Google Scholar
  752. 752.
    Richardson PL, Walsh D, Armi L, Schröder M, Price JF (1989) Tracking three meddies with SOFAR floats. J Phys Oceanogr 19(3):371–383Google Scholar
  753. 753.
    Ridderinkhof H, Loder JW (1994) Lagrangian characterization of circulation over submarine banks with application to the Outer Gulf of Marine. J Phys Oceanogr 24(6):1184–1200Google Scholar
  754. 754.
    Ridderinkhof H, Zimmerman JTF (1992) Chaotic stirring in a tidal system. Science 258(5085):1107–1111Google Scholar
  755. 755.
    Riley JJ, Lelong M-P (2000) Fluid motions in the presence of strong stable stratification. Annu Rev Fluid Mech 32:613–657Google Scholar
  756. 756.
    Ripa P (1989) On the stability of ocean vortices. In: Nihoul JCJ, Jamart BM (eds) Mesoscale/synoptic coherent structures in geophysical turbulence. Elsevier, Amsterdam/Oxford/New York/Tokyo, pp 167–179Google Scholar
  757. 757.
    Ritchie EA, Holland GJ (1993) On the interaction of tropical-cyclone-scale vortices: 2. Discrete vortex patches. Q J R Meteorol Soc 119(514):1363–1379Google Scholar
  758. 758.
    Riser SC, Rossby TH (1983) Quasi-Lagrangian structure and variability of the subtropical western North Atlantic circulation. J Mar Res 42(1):127–162Google Scholar
  759. 759.
    Robinson AR (1996) Physical processes, field estimation and an approach to interdisciplinary ocean modeling. Earth-Sci Rev 40(1–2):3–54Google Scholar
  760. 760.
    Rocío R-M, Viúdez Á, Ruiz S (2011) Vortex merger in oceanic tripoles. J Phys Oceanogr 41(6):1239–1251Google Scholar
  761. 761.
    Rodríguez-Santana A, Pelegrí JL, Sangrá P, Marrero-Díaz A (1999) Diapycnal mixing in Gulf Stream meanders. J Geophys Res 104:25891–25912Google Scholar
  762. 762.
    Rodríguez-Santana A, Pelegrí JL, Sangrá P, Marrero-Díaz A (2001) On the relevance of diapycnal mixing for the stability of frontal meanders. Sci Mar 65(Suppl 1):259–267Google Scholar
  763. 763.
    Rogachev KA, Carmack EC, Foreman MGG (2008) Bowhead whales feed on plankton concentrated by estuarine and tidal currents in Academy Bay, Sea of Okhotsk. Cont Shelf Res 28(14):1811–1826Google Scholar
  764. 764.
    Rogberg P, Dritschel DG (2000) Mixing in two-dimensional vortex interactions. Phys Fluids 12(12):3285 Google Scholar
  765. 765.
    Rogerson AM, Miller PD, Pratt LJ, Jones CKRT (1999) Lagrangian motion and fluid exchange in a barotropic meandering jet. J Phys Oceanogr 29(10):2635–2655Google Scholar
  766. 766.
    Romanov AS (2007) Dipole approximation in three-vortex dynamics. Theor Math Phys 150(3):347–354Google Scholar
  767. 767.
    Romanovskaya ML, Semenova IP, Slezkin LN (2010) Dynamically equilibrium shapes and directions of motion of ocean current rings. J Appl Math Mech 74(3):365–374Google Scholar
  768. 768.
    Roscoe HK, Shanklin JD, Colwell SR (2005) Has the Antarctic Vortex split before 2002? J Atmos Sci 62(3):581–588Google Scholar
  769. 769.
    Rossby CG (1936) Dynamics of steady ocean currents in the light of experimental fluid mechanics. Pap Phys Oceanogr Meteorol 5(1):1–46Google Scholar
  770. 770.
    Rossby T, Dorson D, Fontaine J (1986) The RAFOS system. J Atmos Ocean Tech 3(4):672–679Google Scholar
  771. 771.
    Rossi LF, Lingevitch JF, Bernoff AJ (1997) Quasi-steady monopole and tripole attractors for relaxing vortices. Phys Fluids 9(8):2329–2338Google Scholar
  772. 772.
    Rott N (1989) Three-vortex motion with zero total circulation. J Appl Math Phys (ZAMP) 40(4):473–494Google Scholar
  773. 773.
    Rott N (1990) Constrained three- and four-vortex problems. Phys Fluids A2(8):1477–1480Google Scholar
  774. 774.
    Roullet G, Klein P (2010) Cyclone-anticyclone asymmetry in geophysical turbulence. Phys Rev Lett 104(21):218501. doi:10.1103/PhysRevLett.104.218501Google Scholar
  775. 775.
    Ruddick B (1987) Anticyclonic lenses in large-scale strain and shear. J Phys Oceanogr 17(6):741–749Google Scholar
  776. 776.
    Ruddick B (1992) Intrusive mixing in a Mediterranean salt lens—intrusion slope and dynamical machanisms. J Phys Oceanogr 22(11):1274–1285Google Scholar
  777. 777.
    Ruddick B (2003) Sounding out ocean fine structure. Science 301(5634):772–773Google Scholar
  778. 778.
    Ruddick B, Hebert D (1988) The mixing of meddy “Sharon” In: Nihoul JCJ, Jamart BM (eds) Small-scale mixing in the ocean. Elsevier, New York, pp 249–262Google Scholar
  779. 779.
    Ryzhov EA, Koshel KV (2010) Chaotic transport and mixing of a passive admixture by vortex flows behind obstacles. Izv Atmos Ocean Phys 46(2):184–191Google Scholar
  780. 780.
    Ryzhov EA, Koshel KV (2011) The effect of chaotic advection in a three-layer ocean model. Izv Atmos Ocean Phys 47(2):241–251Google Scholar
  781. 781.
    Ryzhov EA, Koshel KV (2011) Estimating the size of the regular region of a topographically trapped vortex. Geophys Astrophys Fluid Dyn 105(4–5):536–551Google Scholar
  782. 782.
    Ryzhov EA, Koshel KV (2013) Interaction of a monopole vortex with an isolated topographic feature in a three-layer geophysical flow. Nonlinear Process Geophys 20(1):107–119Google Scholar
  783. 783.
    Ryzhov EA, Koshel KV, Stepanov DV (2008) Evaluating the stochastic layer thickness on a two-layer topographic vortex model. Tech Phys Lett 34(6):531–534Google Scholar
  784. 784.
    Ryzhov E, Koshel K, Stepanov D (2010) Background current concept and chaotic advection in an oceanic vortex flow. Theor Comput Fluid Dyn 24(1–4):59–64Google Scholar
  785. 785.
    Sadovskii VS (1971) Vortex regions in a potential stream with a jump of Bernoulli’s constant at the boundary. J Appl Math Mech 35(6):729–735Google Scholar
  786. 786.
    Saenko OA, Zhai X, Merryfield WJ, Lee WG (2012) The combined effect of tidally and eddy-driven diapycnal mixing on the large-scale ocean circulation. J Phys Oceanogr 42(4):526–538Google Scholar
  787. 787.
    Saffman PG (1978) The number of waves on unstable vortex rings. J Fluid Mech 84(4):625–639Google Scholar
  788. 788.
    Saffman PG (1992) Vortex dynamics (Cambridge monographs on mechanics and applied mathematics). Cambridge University Press, Cambridge, 311 ppGoogle Scholar
  789. 789.
    Saffman PG, Baker GK (1979) Vortex interactions. Annu Rev Fluid Mech 11:95–122Google Scholar
  790. 790.
    Saffman P, Schatzman J (1981) Properties of a vortex street of finite vortices. SIAM J Sci Stat Comp 2(3):285–295Google Scholar
  791. 791.
    Saffman P, Schatzman J (1982) An inviscid model for the vortex-street wake. J Fluid Mech 122:467–486Google Scholar
  792. 792.
    Saffman PG, Szeto R (1980) Equilibrium shape of a pair of equal vorteces. Phys Fluids 23(12):2339–2342Google Scholar
  793. 793.
    Saffman PG, Szeto R (1981) Structure of a linear array of uniform vortices. Stud Appl Maths 65:223–248Google Scholar
  794. 794.
    Saffman PG, Tanveer S (1982) The touching pair of equal and opposite uniform vortices. Phys Fluids 25(11):1929–1930Google Scholar
  795. 795.
    Sakamoto K, Akitomo K (2006) Instabilities of the tidally induced bottom boundary layer in the rotating frame and their mixing effect. Dyn Atmos Oceans 41(3–4):191–219Google Scholar
  796. 796.
    Sakamoto T, Yamagata T (1997) Evolution of baroclinic planetary eddies over localized bottom topography in terms of JEBAR. Geophys Asrophys Fluid Dyn 84(1–2):1–27Google Scholar
  797. 797.
    Sakuma H, Ghil M (1991) Stability of propagating modons for small-amplitude perturbations. Phys Fluids A 3(3):408–414Google Scholar
  798. 798.
    Salmon R (1998) Lectures on geophysical fluid dynamics. Oxford University Press, New York, 378 ppGoogle Scholar
  799. 799.
    Samelson RM (1992) Fluid exchange across a meander jet. J Phys Oceanogr 22(4):431–440Google Scholar
  800. 800.
    Samelson RM, Wiggins S (2006) Lagrangian transport in geophysical jets and waves: the dynamical systems approach. Springer Science+Business Media, LLC, New York, 149 ppGoogle Scholar
  801. 801.
    Sangrá P, Pelegrí JL, Hernández-Guerra A, Arregui I, Martín JM, Marrero-Díaz A, Martínez A, Ratsimandresy AW, Rodríguez-Santana A (2005) Life history of an anticyclonic eddy. J Geophys Res 110:C03021. doi:10.1029/2004JC002526Google Scholar
  802. 802.
    Saunders PM (1973) The instability of a baroclinic vortex. J Phys Oceanogr 3(1):61–65Google Scholar
  803. 803.
    Savchenko VG, Emery WJ, Vladimirov OA (1978) A cyclonic eddy in the Antarctic Circumpolar Current south of Australia: results of Soviet-American observations aboard the R/V Professor Zubov. J Phys Oceanogr 8(9):825–837Google Scholar
  804. 804.
    Schär C, Durran DR (1997) Vortex formation and vortex shedding in continuously stratified flows past isolated topography. J Atmos Sci 54(4):534–554Google Scholar
  805. 805.
    Schär C, Smith RB (1993) Shallow-water flow past isolated topography. Part 1. Vorticity production and wake formation. J Atmos Sci 50(10):1373–1400Google Scholar
  806. 806.
    Schultz Tokos KL, Hinrichsen H-H, Zenk W (1994) Merging and migration of two meddies. J Phys Oceanogr 24(10):2129–2141Google Scholar
  807. 807.
    Schultz Tokos K, Rossby T (1991) Kinematics and dynamics of Mediterranean salt lens. J Phys Oceanogr 21(6):879–892Google Scholar
  808. 808.
    Sedov LI (1997) Mechanics of continuous media, vol 2. Word Sci Pub. Co. Pte. Ltd., Singapore, pp 615–1308Google Scholar
  809. 809.
    Selivanova EN (1994) The topology of the problem of three-point vortices. Proc Steklov Inst Math 205:129–137Google Scholar
  810. 810.
    Semenova IP, Slezkin LN (2003) Dynamically equilibrium shape of intrusive vortex formations in the ocean. Fluid Dyn 38(5):663–669Google Scholar
  811. 811.
    Sengupta D, Piterbarg LI, Reznik GM (1992) Localization of topographic Rossby waves over random relief. Dyn Atmos Oceans 17(1):1–21Google Scholar
  812. 812.
    Serra N, Ambar I (2001) Eddy generation in the Mediterranean undercurrent. Deep-Sea Res Part II 49(19):4225–4243Google Scholar
  813. 813.
    Serra N, Sadux S, Ambar I (2002) Observations and laboratory modeling of meddy generation of cape St. Vincent. J Phys Oceanogr 32(1):3–25Google Scholar
  814. 814.
    Shaffer G, Salinas S, Pizarro O, Vega A, Hormazabal S (1995) Currents in the deep ocean off Chile (30 S). Deep Sea Res Part I 42(4):425–436Google Scholar
  815. 815.
    Shapiro GI, Meschanov SL (1996) Spreading pattern and mesoscale structure of Mediterranean outflow in the Iberian Basin estimated from historical data. J Mar Syst 7(2–4):337–348Google Scholar
  816. 816.
    Shapiro GI, Meschanov SL, Emelianov MV (1992) Mediterranean lens after collision with seamounts. Oceanology 32:420–427Google Scholar
  817. 817.
    Shapiro GI, Meschanov SL, Emelianov MV (1995) Mediterranean lens “Irving” after its collision with seamounts. Oceanol Acta 18(3):309–318Google Scholar
  818. 818.
    Shapiro LJ (1992) Hurricane vortex motion and evolution in a three-layer model. J Atmos Sci 49(2):140–154Google Scholar
  819. 819.
    Shapiro LJ (2000) Potential vorticity assymmetry and tropical cyclone evolution in a moist three-layer model. J Atmos Sci 57(21):3645–3662Google Scholar
  820. 820.
    Shavlyugin AI (2011) Two-layer quasi-geostrophic model of contour dynamics for a round basin. Izv Atmos Ocean Phys 47(5):619–627Google Scholar
  821. 821.
    Shaw P-T, Chao S-Y (2003) Effects of a baroclinic current on a sinking dense water plume from a submarine canyon and heton shedding. Deep Sea Res Part I 50(3):357–370Google Scholar
  822. 822.
    Shepherd TG (1990) Symmetries, conservation laws, and Hamiltonian structure in geophysical fluid dynamics. Adv Geophys 32:287–339Google Scholar
  823. 823.
    Shimada K, Kubokawa A (1997) Nonlinear evolution of linearly unstable barotropic boundary currents. J Phys Oceanogr 27(7):1326–1348Google Scholar
  824. 824.
    Shirshov PP (1938) Oceanological observations. Dokl AN USSR 8:569–580 (in Russian)Google Scholar
  825. 825.
    Siedler G, Armi L, Müller TJ (2005) Meddies and decadal changes at the Azores Front from 1980 to 2000. Deep-Sea Res II 52(3–4):583–604Google Scholar
  826. 826.
    Simiu E (1969) Melnikov process for stochastically perturbed, slowly varying oscillators: application to a model of wind-driven coastal currents. J Appl Mech 63(2):429–435Google Scholar
  827. 827.
    Simó C (2001) New families of solutions to the N-body problems. In: Casacuberta C, Miró-Roig RM, Verdera J, Xambó, S (eds) Proceedings of the European 3rd congress of mathematics, vol I (Barcelona, 2000). Progress in mathematics series, vol 201. Birkhäuser, Basel, pp 101–115Google Scholar
  828. 828.
    Simó C (2002) Dynamical properties of the figure eight solution of three-body problem. In: Chenciner A, Cushman R, Robinson C, Xia ZJ (eds) Celestial mechanics, dedicated to Donald Saari for his 60th birthday. Proceedings of the international conference on celestial mechanics, Northwestern University, Evanston, Illinois, 15–19 December 1999. Contemporary Mathematics, vol 292, American Mathematical Society, Providence, pp 209–228Google Scholar
  829. 829.
    Sitnikov IG, Pokhil AE (1998) Interaction of tropical cyclones with each other and with other weather sistems (Part I). Russ Meteorol Hydrol 5:22–28Google Scholar
  830. 830.
    Sitnikov IG, Pokhil AE (1999) Interaction of tropical cyclones with each other and with other weather sistems (Part II). Russ Meteorol Hydrol 7:26–37Google Scholar
  831. 831.
    Skyllingstad ED, Denbo DW (1995) An ocean large-eddy simulation of Langmuir circulations and convection in the surface mixed layer. J Geophys Res 100(C5):8501–8522Google Scholar
  832. 832.
    Smeed DA (1988) Baroclinic instability of three-layer flows: 1. Linear stability. J Fluid Mech 194:217–231Google Scholar
  833. 833.
    Smeed DA (1988) Baroclinic instability of three-layer flows: 2. Experiments with eddies. J Fluid Mech 194:233–259Google Scholar
  834. 834.
    Smith GB, Wei T (1994) Small-scale structure in colliding off-axis vortex rings. J Fluid Mech 259:281–290Google Scholar
  835. 835.
    Smith KS, Marshall J (2009) Evidence for enhanced eddy mixing at middepth in the Southern Ocean. J Phys Oceanogr 39(1):50–69Google Scholar
  836. 836.
    Smith RK (1981) The cyclostrophic adjustment of vortices with application to tropical cyclone modification. J Atmos Sci 38(9):2021–2030Google Scholar
  837. 837.
    Smyth WD, Carpenter JR, Lawrence GA (2007) Mixing in symmetric Holmboe waves. J Phys Oceanogr 37(6):1566–1583Google Scholar
  838. 838.
    Smyth WD, Kimura S (2011) Mixing in a moderately sheared salt-fingering layer. J Phys Oceanogr 41(7):1364–1384Google Scholar
  839. 839.
    Sokolovskiy MA (1986) Numerical modelling of the vortex structure evolution by contour dynamics method. Preprint. Pacific Oceanological Institute of Far East Division of Academy Sciences of USSR, Vladivostok, 19 pp (in Russian)Google Scholar
  840. 840.
    Sokolovskiy MA (1988) Numerical modelling of nonlinear instability for axisymmetric two-layer vortices. Izv Atmos Ocean Phys 24(7):536–542Google Scholar
  841. 841.
    Sokolovskiy MA (1989) Head-on collisions of distributed hetons. Trans Dokl USSR Acad Sci Earth Sci Sect 306(3):215–217Google Scholar
  842. 842.
    Sokolovskiy MA (1990) Numerical modelling of the interaction of distributed hetons during their head-on collisions. In: Kozlov VF (ed) Method of contour dynamics in oceanological investigations. FED USSR Acad Sci, Vladivostok, pp 40–57 (in Russian)Google Scholar
  843. 843.
    Sokolovskiy MA (1990) On the interaction of distributed hetons. Preprint. Pacific Oceanological Institute of Far East Division of Academy Sciences of USSR, Vladivostok, 20 pp (in Russian)Google Scholar
  844. 844.
    Sokolovskiy MA (1991) Modeling triple-layer vortical motions in the ocean by the Contour Dynamics Method. Izv Atmos Ocean Phys 27(5):380–388Google Scholar
  845. 845.
    Sokolovskiy MA (1997) Stability of an axisymmetric three-layer vortex. Izv Atmos Ocean Phys 33(1):16–26Google Scholar
  846. 846.
    Sokolovskiy MA (1997) Stability analysis of the axisymmetric three-layered vortex using contour dynamics method. Comput Fluid Dyn J 6(2):133–156Google Scholar
  847. 847.
    Sokolovskiy MA, Carton X (2010) Baroclinic multipole formation from heton interaction. Fluid Dyn Res 42:045501. doi:10.1088/0169-5983/42/4/045501Google Scholar
  848. 848.
    Sokolovskiy MA, Filyushkin BN, Carton X (2013) Dynamics of intrathermocline vortices in a gyre flow over a seamount chain. Ocean Dyn 63. doi:10.1007/s10236-013-0628-yGoogle Scholar
  849. 849.
    Sokolovskiy MA, Koshel KV, Carton X (2011) Baroclinic multipole evolution in shear and strain. Geophys Asrophys Fluid Dyn 105(4–5):506–535Google Scholar
  850. 850.
    Sokolovskiy MA, Koshel KV, Verron J (2013) Three-vortex quasi-geostrophic dynamics in a two-layer fluid. Part 1. Analysis of relative and absolute motions. J Fluid Mech 717:232–254Google Scholar
  851. 851.
    Sokolovskiy MA, Verron J (2000) Finite-core hetons: stability and interactions. J Fluid Mech 423:127–154Google Scholar
  852. 852.
    Sokolovskiy MA, Verron J (2000) Four-vortex motion in the two layer approximation: integrable case. Regul Chaotic Dyn 5(4):413–436Google Scholar
  853. 853.
    Sokolovskiy MA, Verron J (2002) Dynamics of the triangular two-layer vortex structures with zero total intensity. Regul Chaotic Dyn 7(4):435–472Google Scholar
  854. 854.
    Sokolovskiy MA, Verron J (2002) New stationary solutions to the problem of three vortices in a two-layer fluid. Dokl Phys 47(3):233–237Google Scholar
  855. 855.
    Sokolovskiy MA, Verron J (2004) Dynamics of the three vortices in two-layer rotating fluid. Regul Chaotic Dyn 9(4):417–438Google Scholar
  856. 856.
    Sokolovskiy MA, Verron J (2006) Some properties of motion of A + 1 vortices in a two-layer rotating fluid. Russ Sci J Nonlinear Dyn 2(1):27–54 (in Russian)Google Scholar
  857. 857.
    Sokolovskiy MA, Verron J (2008) Motion of A + 1 vortices in a two-layer rotating fluid. In: Borisov AV, Kozlov VV, Mamaev IS, Sokolovskiy MA (eds) IUTAM symposium on hamiltonian dynamic, vortex strictures, turbulence (IUTAM Bookseries, vol 6). Springer, New York, pp 481–490Google Scholar
  858. 858.
    Sokolovskiy MA, Verron J (2011) Dynamics of vortex structures in a stratified rotating fluid. Moscow-Izhevsk, Izhevsk Institution of Computer Science, 372 pp (in Russian)Google Scholar
  859. 859.
    Sokolovskiy M, Verron J, Carton X, Gryanik V (2010) On instability of elliptical hetons. Theor Comput Fluid Dyn 24(1–4):117–123Google Scholar
  860. 860.
    Sokolovskiy MA, Verron J, Vagina IM (2001) Effect of a submerged small-height obstacle on the dynamics of a distributed heton. Izv Atmos Ocean Phys 37(1):122–133Google Scholar
  861. 861.
    Sokolovskiy MA, Zyryanov VN, Davies PA (1998) On the influence of an isolated submerged obstacle on a barotropic tidal flow. Geophys Astrophys Fluid Dyn 88(1):1–30Google Scholar
  862. 862.
    Solomon TH, Weeks ER, Swinney HL (1994) Chaotic advection in a two-dimensional flow: Lévy flights and anomalous diffusion. Phys D 76(1–3):70–84Google Scholar
  863. 863.
    Spall MA (1994) Mechanism for low-frequency variability and salt flux in Mediterranean salt tongue. J Geophys Res 99(C5):10121–10129Google Scholar
  864. 864.
    Spall MA, Chapman DC (1998) On the efficiency of baroclinic eddy heat transport across narrow fronts. J Phys Oceanogr 28(11):2275–2287Google Scholar
  865. 865.
    Spall MA, Richardson PL, Price J (1993) Advection and eddy mixing in the Mediterranean salt tongue. J Mar Res 51(4):797–818Google Scholar
  866. 866.
    Spohn A, Mory M, Hopfinger EJ (1993) Observations of vortex breakdown in an open cylindrical container with a rotating bottom. Exp Fluids 14(1–2):70–77Google Scholar
  867. 867.
    Spohn A, Mory M, Hopfinger EJ (1998) Experiments on vortex breakdown in a confined flow generated by a rotating disc. J Fluid Mech 370:73–99Google Scholar
  868. 868.
    Stammer D (1998) On eddy characteristics, eddy transports, and mean flow properties. J Phys Oceanogr 28(4):727–739Google Scholar
  869. 869.
    Stammer D, Hinrichsen H-H, Käse RH (1991) Can meddies be detected by satellite altimetry? J Geophys Res 96(C4):7005–7014Google Scholar
  870. 870.
    Stammer D, Wunsch C, Neyoshi K (2006) Temporal changes in ocean eddy transport. J Phys Oceanogr 36(3):543–550Google Scholar
  871. 871.
    Stegner A, Zeitlin V (1996) Asymptotic expansions and monopolar solitary Rossby vortices in barotropic and two-layer models. Geophys Astrophys Fluid Dyn 83(3–4):159–194Google Scholar
  872. 872.
    Stern ME (1975) Minimal properties of planetery eddies. J Mar Res 33(1):1–13Google Scholar
  873. 873.
    Stern ME (2000) Scattering of an eddy advected by a current towards a topographic obstacle. J Fluid Mech 402:211–223Google Scholar
  874. 874.
    Stewart KD, Hughes GO, Griffiths RW (2012) The role of turbulent mixing in an overturning circulation maintained by surface buoyancy forcing. J Phys Oceanogr 42(11):1907–1922Google Scholar
  875. 875.
    Stirling JR (2003) Chaotic advection, transport and patchiness in clouds of pollution in an estuarine flow. Discret Contin Dyn Syst Ser B 3(2):263–284Google Scholar
  876. 876.
    Stremler MA, Aref H (1999) Motion of three point vortices in a periodic parallelogram. J Fluid Mech 392:101–128Google Scholar
  877. 877.
    Su CH (1979) Motion of fluid with constant vorticity in a singly-connected region. Phys Fluids 22(10):2032–2033Google Scholar
  878. 878.
    Sutyrin GG, Herbette S, Carton X (2011) Deformation and splitting of baroclinic eddies encountering a tall seamount. Geophys Astrophys Fluid Dyn 105(4–5):478–505Google Scholar
  879. 879.
    Sutyrin GG, Hesthaven JS, Lynov JP, Rasmussen JJ (1994) Dynamical properties of vortical structures on the beta-plane. J Fluid Mech 268:103–131Google Scholar
  880. 880.
    Sutyrin GG, McWilliams JC, Saravanan R (1998) Co-rotating stationary states and vertical alignment of geostrophic vortices with thin cores. J Fluid Mech 357:321–349Google Scholar
  881. 881.
    Sutyrin GG, Perrot X, Carton X (2008) Integrable motion of a vortex dipole in an axisymmetric flow. Phys Lett 372A:5452–5457Google Scholar
  882. 882.
    Sutyrin GG, Stegner A, Taupier-Letage I, Teinturier S (2009) Amplification of a surface-intensified eddy drift along a steep shelf in the Eastern Mediterranean Sea. J Phys Oceanogr 39(7):1729–1741Google Scholar
  883. 883.
    Swallow JG (1969) A deep eddy off Cape St. Vincent. Deep-Sea Res 16(Suppl):285–295Google Scholar
  884. 884.
    Swaters GE (1986) Stability conditions and apriori estimates for equivalent barotropic modons. Phys Fluids 29(5):1419–1422Google Scholar
  885. 885.
    Swenson M (1987) Instability of equivalent-barotropic riders. J Phys Oceanogr 17(4):492–506Google Scholar
  886. 886.
    Synge J (1949) On the motion of three vortices. Can J Math 1:257–270Google Scholar
  887. 887.
    Tailleux R (2012) On the generalized eigenvalue problem for the Rossby wave vertical velocity in the presence of mean flow and topography. J Phys Oceanogr 42(6):1045–1050Google Scholar
  888. 888.
    Takahashi J, Masuda A (1998) Mechanisms of the southward translation of meddies. J Oceanogr 54(6):669–680Google Scholar
  889. 889.
    Tan B, Boyd JP (1977) Dynamics of the Flierl-Petviashvili monopoles in a barotropic model with topographic forcing. Wave Motion 26(3):239–251Google Scholar
  890. 890.
    Tang B, Cushman-Roisin B (1992) Two-layer geostrophic dynamics: 2. Geostrophic turbulence. J Phys Oceanogr 22(2):128–138Google Scholar
  891. 891.
    Tansley CE, Marshall DP (2000) On the influence of bottom topography and the Deep Western Boundary Current on Gulf Stream separation. J Mar Res 58(2):297–325Google Scholar
  892. 892.
    Tavantzis J, Ting L (1988) The dynamics of three vortices revisited. Phys Fluids 31(6):1392–1409Google Scholar
  893. 893.
    Taylor GI (1921) Experiments with rotating fluids. Proc R Soc Ser A 100:114–121Google Scholar
  894. 894.
    Taylor GI (1923) Experiments on the motion of solid bodies in rotating fluids. Proc R Soc Ser A 104:213–218Google Scholar
  895. 895.
    Tél T, Gruiz M (2006) Chaotic dynamics. An introduction based on classical mechanics. Cambridge University Press, Cambridge, 412 ppGoogle Scholar
  896. 896.
    Temam R, Ziane M (2005) Some mathematical problems in geophysical fluid dynamics. In: Friedlander S, Serre D (eds) Handbook of mathematical fluid dynamics, vol 3. Elsevier, New York, pp 535–658Google Scholar
  897. 897.
    Tevs MV (1999) Kinematic study of the vertical structure of tropical cyclones on the basis of an N-level quasi-geostrophic atmospheric model. Izv Atmos Ocean Phys 35(4):435–439Google Scholar
  898. 898.
    Thierry V, Morel Y (1999) Influence of a strong bottom slope on the evolution of a surface-intensified vortex. J Phys Oceanogr 29(5):911–924Google Scholar
  899. 899.
    Thivolle-Cazat E, Sommeria J, Galmiche M, Verron J (2001) An experimental investigation of heton instability in a rotating, two-layer fluid. In: Chashechkin YuD (ed) Proceedings of the Moscow international conference on fluxes and structures in fluids, Institute for Problems in Mechanics of RAS, Moscow, pp 205–206Google Scholar
  900. 900.
    Thivolle-Cazat E, Sommeria J, Galmiche M (2005) Baroclinic instability of two-layer vortices in laboratory experiments. J Fluid Mech 544:69–97Google Scholar
  901. 901.
    Thompson AF, Sallée J-B (2012) Jets and topography: jet transitions and the impact on transport in the Antarctic Circumpolar Current. J Phys Oceanogr 42(6):956–972Google Scholar
  902. 902.
    Thompson L (1993) Two-layer quasigeostrophic flow over finite isolated topography. J Phys Oceanogr 23(7):1297–1314Google Scholar
  903. 903.
    Thompson L, Flierl GR (1993) Barotropic flow over finite isolated topography: steady solutions on the beta-plane and the initial value problem. J Fluid Mech 250:553–586Google Scholar
  904. 904.
    Thomson W (Lord Kelvin) (1875) Vortex statics. Math Phys Pap IV:115–128Google Scholar
  905. 905.
    Thomson W (Lord Kelvin) (1887) On the stability of steady and of periodic fluid motion. Philos Mag ser 5. 23(144):459–469Google Scholar
  906. 906.
    Tilburg CE, Hurlburt HE, O’Brien JJ, Shriver JF (2002) Remote topographic forcing of a baroclinic western boundary current: an explanation for the Southland Current and the pathway of the subtropical front east of New Zealand. J Phys Oceanogr 32(11):3216–3232Google Scholar
  907. 907.
    Tkachenko VK (1966) On vortex lattices. Sov Phys JETP 22(6):1282–1286Google Scholar
  908. 908.
    Tkachenko VK (1966) Stability of vortex lattices. Sov Phys JETP 23(6):1049–1056Google Scholar
  909. 909.
    Trieling RR, van Heijst GJF, Kizner Z (2010) Laboratory experiments on multipolar vortices in a rotating fluid. Phys Fluids 22(9):094104. doi:10.1063/1.3481797Google Scholar
  910. 910.
    Trieling RR, Velasco Fuentes OU, van Heijst GJFR (2005) Interaction of two unequal corotating vortices. Phys Fluids 17(8):087103. doi:10.1063/1.1993887Google Scholar
  911. 911.
    Tritton DJ (1988) Physical fluid dynamics. Clarendon Press, Oxford, 536 ppGoogle Scholar
  912. 912.
    Tronin KG (2006) Absolute choreographies of point vortices on a sphere. Regul Chaotic Dyn 11(1):123–130Google Scholar
  913. 913.
    Turkington B (1985) Corotating steady vortex flows with N-fold symmetry. Nonlinear Anal Theor Methods Appl 9(4):351–369Google Scholar
  914. 914.
    Tychensky A, Carton X (1998) Hydrological and dynamical characterization of meddies in the Azores region: a paradigm for baroclinic vortex dynamics. J Geophys Res 103(C11):25061–25079Google Scholar
  915. 915.
    Tychensky A, Le Traon P-Y, Hernandez F, Jourdan D (1998) Large structures and temporal change in the Azores Front during the SEMAPHORE experiment. J Geophys Res 103(C11):25009–25027Google Scholar
  916. 916.
    Uleysky MYu, Budyansky MV, Prants SV (2007) Effect of dynamical traps on chaotic transport in a meandering jet flow. Chaos 17(4):043105. doi:10.1063/1.2783258Google Scholar
  917. 917.
    Uleysky MYu, Budyansky MV, Prants SV (2008) Genesis and bifurcations of unstable periodic orbits in a jet flow. J Phys A Math Theor 41(2):215102. doi:10.1088/1751-8113/41/21/215102Google Scholar
  918. 918.
    Uleysky MYu, Budyansky MV, Prants SV (2010) Mechanism of destruction of the transport barriers in geophysical jets with Rossby waves. Phys Rev E 81(1):017202. doi:10.1103/PhysRevE.81.017202Google Scholar
  919. 919.
    Valcke S, Verron J (1993) On interactions between two finite-core hetons. Phys Fluids A5(8):2058–2060Google Scholar
  920. 920.
    Valcke S, Verron J (1996) Cyclone-anticyclone asymmetry in the merging process. Dyn Atmos Oceans 24(1–4):227–236Google Scholar
  921. 921.
    Valcke S, Verron J (1997) Interactions of baroclinic isolated vortices: the dominant effect of shielding. J Phys Oceanogr 27(4):524–541Google Scholar
  922. 922.
    Vallis GK (2006) Atmospheric and oceanic fluid dynamics: fundamentals and large-scale circulation. Cambridge University Press, Cambridge, 745 ppGoogle Scholar
  923. 923.
    Vandermeirsch FO, Carton XJ, Morel YG (2003) Interaction between an eddy and a zonal jet. Part I. One-and-a-half-layer model. Dyn Atmos Oceans 36(4):247–270Google Scholar
  924. 924.
    Vandermeirsch FO, Carton XJ, Morel YG (2003) Interaction between an eddy and a zonal jet. Part II. Two-and-a-half-layer model. Dyn Atmos Oceans 36(4):271–296Google Scholar
  925. 925.
    Vandermeirsch F, Morel Y, Sutyrin G (2001) The net convective effect of a vertically sheared current on a coherent vortex. J Phys Oceanogr 31(8):2210–2225Google Scholar
  926. 926.
    Vandermeirsch F, Morel Y, Sutyrin G (2002) Resistance of a coherent vortex to a vertical shear. J Phys Oceanogr 32(11):3089–3100Google Scholar
  927. 927.
    van der Toorn R, Zimmerman JTF (2010) Angular momentum dynamics and the intrinsic drift of monopolar vortices on a rotating sphere. J Math Phys 51(8):083102. doi:10.1063/1.3455315Google Scholar
  928. 928.
    van Geffen JHGM, Davies PA (1999) Interaction of a monopolar vortex with a topographic ridge. Geophys Astrophys Fluid Dyn 90(1–2):1–41Google Scholar
  929. 929.
    van Geffen JHGM, Davies PA (2000) A monopolar vortex encounters a north-south ridge or trough. Fluid Dyn Res 26(3):157–179Google Scholar
  930. 930.
    van Geffen JHGM, Davies PA (2000) A monopolar vortex encounters an isolated topographic feature on a β-plane. Dyn Atmos Oceans 32(1):1–26Google Scholar
  931. 931.
    Van-Dyke M (1982) An album of fluid motion. Parabolic Press, Stanford.Google Scholar
  932. 932.
    van Heijst GJF (1994) Topography effects on vortices in a rotating fluid. Meccanica 29(4):431–451Google Scholar
  933. 933.
    van Heijst GJF, Clercx HJH (2009) Laboratory modeling of geophysical vortices. Annu Rev Fluid Mech 41:143–164Google Scholar
  934. 934.
    van Heijst GJF, Flór JB (1989) Laboratory experiments on dipole structures in a stratified fluids. In: Nihoul JCJ, Jamart BM (eds) Mesoscale/synoptic coherent structures in geophysical turbulence. Elsevier, Amsterdam/Oxford/New York/Tokyo, pp 591–608Google Scholar
  935. 935.
    van Heijst GJF, Kloosterziel RC (1989) Tripolar vortices in a rotating fluid. Nature 338:569–571Google Scholar
  936. 936.
    van Heijst GJF, Kloosterziel RC, Williams CWM (1991) Laboratory experiments on the tripolar vortex in a rotating fluid. J Fluid Mech 225:301–331Google Scholar
  937. 937.
    Velasco Fuentes OU (1994) Propagation and transport properties of dipolar vortices on a γ plane. Phys Fluids 6(10):3341–3352Google Scholar
  938. 938.
    Velasco Fuentes OU (2001) Chaotic advection by two interacting finite-area vortices. Phys Fluids 13(4):901–912Google Scholar
  939. 939.
    Velasco Fuentes OU, van Heijst GJF (1994) Experimental study of dipolar vortices on a topographic β-plane. J Fluid Mech 259:79–106Google Scholar
  940. 940.
    Velasco Fuentes OU, van Heijst GJF, Cremers BE (1995) Chaotic transport by dipolar vortices on the β-plane. J Fluid Mech 291:139–161Google Scholar
  941. 941.
    Velasco Fuentes OU, van Heijst GJF, van Lipzing NPM (1996) Unsteady behaviour of a topography-modulated tripole. J Fluid Mech 307:11–41Google Scholar
  942. 942.
    Venaille A (2012) Bottom-trapped currents as statistical equilibrium states above topographic anomalies. J Fluid Mech 699:500–510Google Scholar
  943. 943.
    Verron J (1986) Topographic eddies in temporally varying oceanic flows. Geophys Astophys Fluid Dyn 35(1–4):257–276Google Scholar
  944. 944.
    Verron J, Hopfinger E (1991) The enigmatic merging conditions of two-layer baroclinic vortices. C R Acad Sci Paris Ser II 313(7):737–742Google Scholar
  945. 945.
    Verron J, Hopfinger E, McWilliams JC (1990) Sensitivity to initial conditions in the merging of two-layer baroclinic vortices. Phys Fluids A2(6):886–889Google Scholar
  946. 946.
    Verron J, Le Provost C (1985) A numerical study of quasigeostrophic flow over isolated topography. J Fluid Mech 154:231–252Google Scholar
  947. 947.
    Verron J, Le Provost C, Holland WR (1987) On the effects of a midocean ridge on the general circulation: numerical simulations with an eddy-resolved ocean model. J Phys Oceanogr 17(3):301–312Google Scholar
  948. 948.
    Verron J, Valcke S (1994) Scale-dependent merging of baroclinic vortices. J Fluid Mech 264:81–106Google Scholar
  949. 949.
    Vilela RD, de Moura APS, Grebory C (2006) Finite-size effects on open chaotic advection. Phys Rev E 73:026302. doi:10.1103/PhysRevE.73.026302Google Scholar
  950. 950.
    Villat H (1930) Leçons sur la théorie des tourbillons. Gauthier-Villars et cie, Paris, 300 ppGoogle Scholar
  951. 951.
    Visbeck M, Marshall J, Haine T, Spall M (1997) On the specification of eddy transfer coefficients in coarse-resolution ocean circulation models. J Phys Oceanogr 27(3):381–402Google Scholar
  952. 952.
    Visbeck M, Marshall J, Jones H (1996) Dynamics of isolated convective regions in the ocean. J Phys Oceanogr 26(9):1721–1734Google Scholar
  953. 953.
    Visheratin KN, Kalashnik MV (2007) Cyclostrophic adjustment and cooling processes in Ranque-vortex tube. Int J Low-Carbon Tech 2(1):10–19Google Scholar
  954. 954.
    Viúdez A (2010) Vertical splitting of vortices in geophysical dipoles. J Phys Oceanogr 40(9):2170–2179Google Scholar
  955. 955.
    von Hardenberg J, McWilliams JC, Provenzale A, Shchepetkin A, Weiss JB (2000) Vortex merging in quasi-geostrophic flows. J Fluid Mech 412:331–353Google Scholar
  956. 956.
    Voropayev SI (1992) Mushroom-like currents: the laboratory experiments, theory, numerical calculations. In: Barenblatt GI, Seidov DG, Sutyrin GG (eds) Coherent structures and self-organisation of currents in the ocean. Nauka, Moscow, pp 177–189 (in Russian)Google Scholar
  957. 957.
    Voropayev SI, Afanasyev YaD (1992) Two-dimensional vortex-dipole interactions in a stratified fluid. J Fluid Mech 236:665–689Google Scholar
  958. 958.
    Vosbeek PWC, van Heijst GJF, Mogendorff VP (2001) The strain rate in evolution of elliptical vortices in inviscid two-dimensional flows. Phys Fluids 13(12):3699–3708Google Scholar
  959. 959.
    Vranješ J, Marić G, Shukla PK 1999) Tripolar vortices and vortex chains in dusty plasma. Phys Lett A 258(4–6):317–322Google Scholar
  960. 960.
    Vranješ J, Okamoto A, Yoshimura S, Poedts S, Kono M, Tanaka MY (2002) Analytical description of a neutral-induced tripole vortex in a plasma. Phys Rev Lett 89(26). doi:10.1103/PhysRevLett.89.265002Google Scholar
  961. 961.
    Vranješ J, Stenflo L, Shukla PK (2000) Tripolar vortices and vortex chains in a shallow atmosphere. Phys Lett A 267(2–3):184–187Google Scholar
  962. 962.
    Vukovich FM, Waddell E (1991) Interaction of a warm core ring with the western slope in the Gulf of México. J Phys Oceanogr 21(7):1062–1074Google Scholar
  963. 963.
    Waite ML, Smolarkiewicz PK (2008) Instability and breakdown of a vertical vortex pair in a strongly stratified fluid. J Fluid Mech 606:239–273Google Scholar
  964. 964.
    Wåhlin AK (2004) Topographic advection of dense bottom water. J Fluid Mech 510:95–104Google Scholar
  965. 965.
    Walsh D, Pratt LJ (1995) The interaction of a pair of point potential vortices in uniform shear. Dyn Atmos Oceans 22(3):135–160Google Scholar
  966. 966.
    Wan Y-H (1986) The stability of rotating vortex patches. Commun Math Phys 107(1):1–20Google Scholar
  967. 967.
    Wan Y-H, Pulvirenti M (1985) Nonlinear stability of circular vortex patches. Commun Math Phys 99(3):435–450Google Scholar
  968. 968.
    Wang GH, Dewar WK (2003) Meddy-seamount interactions: Implications for the Mediterranean salt tongue. J Phys Oceanogr 33(11):2446–2461Google Scholar
  969. 969.
    Warren BA, Wunsch C (1981) Evolution of physical oceanography. MIT Press, Cambridge, 623 ppGoogle Scholar
  970. 970.
    Waseda T, Mitsudera H (2002) Chaotic advection of the shallow Kuroshio coastal waters. J Oceanogr 58(5):627–638Google Scholar
  971. 971.
    Waseda T, Mitsudera H, Taguchi B, Yoshikawa Y (2002) On the eddy-Kuroshio interaction: evolution of the mesoscale eddy. J Geophys Res. doi:10.1029/2000JC000756Google Scholar
  972. 972.
    Waugh DW (1992) The efficiency of symmetric vortex merger. Phys Fluids A 4(8):1745–1758Google Scholar
  973. 973.
    Waugh DW (1993) Subtropical stratospheric mixing linked to distubances in the polar vortices. Nature 365(6446):535–537Google Scholar
  974. 974.
    Waugh DW, Keating SR, Chen M-L (2012) Diagnosing ocean stirring: comparison of relative dispersion and finite-time Lyapunov exponents. J Phys Oceanogr 42(35):1173–1185Google Scholar
  975. 975.
    Welander P (1955) Studies of the general development of motion in a two-dimensional, ideal fluid. Tellus 7(2):141–156Google Scholar
  976. 976.
    White AJ, McDonald NR (2004) The motion of a point vortex near large- amplitude topography in a two-layer fluid. J Phys Oceanogr 34(12):2808–2824Google Scholar
  977. 977.
    Whitehead JA (1995) Thermohaline ocean processes and models. Annu Rev Fluid Mech 27:89–113Google Scholar
  978. 978.
    Whitehead JA, Marshall J, Hufford GE (1996) Localized convection in a rotating stratified fluid. J Geophys Res 101(C10):25705–25721Google Scholar
  979. 979.
    Whitehead JA, Wang W (2008) A laboratory model of vertical ocean circulation driven by mixing. J Phys Oceanogr 38(5):1091–1106Google Scholar
  980. 980.
    Widnall SE, Sullivan JP (1973) On the stability of vortex rings. Proc R Soc Lond A 332:335–353Google Scholar
  981. 981.
    Wiggins S (2005) The dynamical systems approach to Lagrangian transport in oceanic flows. Annu Rev Fluid Mech 37:295–328Google Scholar
  982. 982.
    Winant CD, Browand FK (1974) Vortex pairing: the mechanism of turbulent mixing-layer growth at moderate Reynolds number. J Fluid Mech 63(2):237–255Google Scholar
  983. 983.
    Wirth A (2000) The parametrization of baroclinic instability in a simple model. J Mar Res 58(4):571–583Google Scholar
  984. 984.
    Wirth A, Barnier B (2008) Mean circulation and structures of tilted ocean deep convection. J Phys Oceanogr 38(4):803–816Google Scholar
  985. 985.
    Woodgate RA, Aagaard K, Muench RD, Gunn J, Björk G, Rudels B, Roach AT, Schauer U (2001) The Arctic ocean boundary current along the Eurasian slope and the adjacent Lomonosov Ridge: water mass properties, transports and transformations from moored instruments. Deep Sea Res I 48(8):1757–1792Google Scholar
  986. 986.
    Wu HM, Overman EA II, Zabusky NJ (1984) Steady-state solutions of the Euler equations: rotating and translating V-states with limiting cases. I. Numerical algorithms and results. J Comput Phys 53(1):42–71Google Scholar
  987. 987.
    Wu J-Z, Ma H-Y, Zhou M-D (2006) Vorticity and vortex dynamics. Springer, Berlin/Heidelberg 776 ppGoogle Scholar
  988. 988.
    Wunsch C, Ferrari R (2004) Vertical mixing, energy, and the general circulation of the oceans. Annu Rev Fluid Mech 36:281–314Google Scholar
  989. 989.
    Wüst G (1935) Schichtung und zirculation des Atlantischen Ozean. Die Stratosphäre. Exped. “Meteor” 1925–27. Wiss Ergeb Bd 6(1):106 ppGoogle Scholar
  990. 990.
    Yang H (1993) Chaotic mixing and transport in wave systems and atmosphere. Int J Bifurc Chaos 3(6):1423–1445Google Scholar
  991. 991.
    Yang H (1996) Chaotic transport and mixing by ocean gyre circulation. In: Adler J, Muller P, Rozovskii B (eds) Stochastic modeling in physical oceanography. Birkhauser, Boston, pp 439–466Google Scholar
  992. 992.
    Yang H (1996) The subtropical/subpolar gyre exchange in the presence of annually migrating wind and meandering jet: water mass exchange. J Phys Oceanogr 26(1):115–139Google Scholar
  993. 993.
    Yang H (1996) Lagrangian modeling of potential vorticity homogenization and the associated front in the Gulf Stream. J Phys Oceanogr 26(11):2480–2496Google Scholar
  994. 994.
    Yang H (1998) The central barrier, asymmetry and random phase in chaotic transport and mixing by Rossby waves in a jet. Int J Bifurc Chaos 8(6):1131–1152Google Scholar
  995. 995.
    Yang H, Liu Z (1994) Chaotic transport in a double gyre ocean. Geophys Res Lett 21(7):545–548Google Scholar
  996. 996.
    Yang H, Liu Z (1997) The three-dimensional chaotic transport and the great ocean barrier. J Phys Oceanogr 27(7):1258–1273Google Scholar
  997. 997.
    Yasuda I (1995) Geostrophic vortex merger and streamer development in the ocean with special reference to the merger of Kuroshio warm core ring. J Phys Oceanogr 25(5):979–996Google Scholar
  998. 998.
    Yasuda I, Flierl GR (1995) Two-dimensional asymmetric vortex merger: contour dynamics experiment. J Oceanogr 51(2):145–170Google Scholar
  999. 999.
    Yasuda I, Flierl GR (1997) Two-dimensional asymmetric vortex merger: merger dynamics and critical merger distance. Dyn Atmos Oceans 26(3):159–181Google Scholar
  1000. 1000.
    Yatsuyanagi Y, Hatori T, Kato T (2001) Chaotic reconnection due to fast mixing of vortex-current filaments. Earth Planets Space 53:615–618Google Scholar
  1001. 1001.
    Yegorikhin VD, Ivanov YA, Kort VG, Koshlyakov MN, Lukashev YF, Morozov EG, Ovchinnikov IM, Paka VT, Tsybaneva TB, Shadrin IF, Shapovalov SM (1987) An intrathermocline lens of Mediterranean water in the tropical North Atlantic. Oceanology 27(2):121–127Google Scholar
  1002. 1002.
    Yemel’yanov MN, Fedorov KN (1985) Structure and transformation of intermediate waters of the Mediterranean Sea and Atlantic Ocean. Oceanology 25(2):155–161Google Scholar
  1003. 1003.
    Young WR (1985) Some interactions between small numbers of baroclinic, geostrophic vortices. Geophys Astrophys Fluid Dyn 33(1–4):35–61Google Scholar
  1004. 1004.
    Youssef A, Marcus PS (2003) The dynamics of Jovian white ovals from formation to merger. Icarus 162(1):74–93Google Scholar
  1005. 1005.
    Yuan G-C, Pratt LJ, Jones CKRT (2002) Barrier destruction and Lagrangian predictability at depth in a meandering jet. Dyn Atmos Oceans 35(1):41–61Google Scholar
  1006. 1006.
    Zabusky NJ, Hughes MH, Roberts KV (1979) Contour dynamics for the Euler equations in two dimensions. J Comput Phys 30(1):96–106Google Scholar
  1007. 1007.
    Zaslavsky GM (2007) The physics of chaos in Hamiltonian systems, 2nd edn. Imperial College Press, London, 315 ppGoogle Scholar
  1008. 1008.
    Zatsepin AG, Ginzburg AI, Kostyanoy AG, Kremenetskiy VV, Krivosheya VG, Stanichny SV, Poulain P-M (2003) Observation of Black Sea mesoscale eddies and associated horizontal mixing. J Geophys Res 108(C8):3246. doi:10.1029/2002JC001390Google Scholar
  1009. 1009.
    Zatsepin AG, Kostyanoy AG (1992) Laboratory study of the instability of baroclinic eddies and fronts. In: Barenblatt GI, Seidov DG, Sutyrin GG (eds) Coherent structures and self-organisation of currents in the ocean. Nauka, Moscow, pp 163–177 (in Russian)Google Scholar
  1010. 1010.
    Zavala Sansón L (2000) The effects of topography on rotating barotropic flows. Proefschrift. Technische Universiteit Eindhoven, Eindhoven, 152 ppGoogle Scholar
  1011. 1011.
    Zavala Sansoón L (2002) Vortex-ridge interaction in a rotating fluid. Dyn Atmos Oceans 35(4):299–325Google Scholar
  1012. 1012.
    Zavala Sansón L (2010) Solutions of barotropic trapped waves around seamounts. J Fluid Mech 661:32–44Google Scholar
  1013. 1013.
    Zavala Sansón L, Aguiar ACB, van Heijst GJF (2012) Horizontal and vertical motions of barotropic vortices over a submarine mountain. J Fluid Mech 695:173–198Google Scholar
  1014. 1014.
    Zavala Sansón L, van Heijst GJF (2000) Interaction of barotropic vortices with coastal topographies: laboratory experiments and numerical simulation. J Phys Oceanogr 30(9):2141–2162Google Scholar
  1015. 1015.
    Zavala Sansón L, van Heijst GJF (2002) Ekman effects in a rotating flow over bottom topography. J Fluid Mech 471:239–255Google Scholar
  1016. 1016.
    Zehnder JA (1993) The influence of large-scale topography on barotropic vortex motion. J Atmos Sci 50(15):2519–2532Google Scholar
  1017. 1017.
    Zelenko AA, Resnyansky YuD (2007) Deep convection in the ocean general circulation model: variability on the diurnal, seasonal, and interannual time scales. Oceanology 47(2):191–204Google Scholar
  1018. 1018.
    Zeng X, Pielke RA, Eykholt R (1993) Chaos theory and its applications to the atmosphere. Bull Am Meteorol Soc 74(4):631–644Google Scholar
  1019. 1019.
    Zenk W, Schultz Tokos K, Boebel O (1992) New observations of meddy movement south of the Tejo Plateau. Geophys Res Lett 12(24):2389–2392Google Scholar
  1020. 1020.
    Zhikharev G (1989) Stability of steady circulation regims with a nonzonal mean flow over wary topography in a barotropic model of the open ocean. J Phys Oceanogr 19(3):392–395Google Scholar
  1021. 1021.
    Zhikharev GM (1990) On steady and travelling waves over bottom topography in the model of homogeneous flow in a beta-plane channel. Geophys Astrophys Fluid Dyn 54(3–4):159–279Google Scholar
  1022. 1022.
    Zhikharev GM (1994) On steady quasi-geostrophic flow component formation over undulating bottom topography: Part I. Low-order and direct numerical simulations of homogeneous flows. Geophys Astrophys Fluid Dyn 74(1–4):99–122Google Scholar
  1023. 1023.
    Zhikharev GM (1995) On steady quasi-geostrophic flow component formation over undulating bottom topography: Part II. A two-layer low-order model of the open ocean. Geophys Astrophys Fluid Dyn 80(3–4):145–166Google Scholar
  1024. 1024.
    Zhmur VV (2011) Mesoscale ocean eddies. GEOS, Moscow, 290 pp (in Russian)Google Scholar
  1025. 1025.
    Zhmur VV, Pankratov KK (1990) Distant interaction for an ensemble of quasigeostrophic eddies. The hamiltonian formulation. Izv Atmos Ocean Phys 26(9):714–720Google Scholar
  1026. 1026.
    Zhmur VV, Ryzhov EA, Koshel KV (2011) Ellipsoidal vortex in a nonuniform flow: dynamics and chaotic advection. J Mar Res 69(2–3):435–461Google Scholar
  1027. 1027.
    Zhmur VV, Shchepetkin AF (1991) Evolution of an ellipsoidal vortex in a stratified ocean in the f-plane approximation. Izv Atmos Ocean Phys 27(5):337–345Google Scholar
  1028. 1028.
    Zhmur VV, Shchepetkin AF (1992) Interaction between two quasigeostrophic baroclinic vortices: tendency to come together and merge. Izv Atmos Ocean Phys 28(5):407–417Google Scholar
  1029. 1029.
    Zhurbas VM, Oh IS, Pyzhevich ML (2003) Maps of horizontal diffusivity and Lagrangian scales in the Pacific Ocean obtained from drifter data. Oceanology 43(5):622–631Google Scholar
  1030. 1030.
    Ziglin SL (1980) Nonintegrability of the problem on the motion of four point vortices. Sov Math Dokl 21:296–299Google Scholar
  1031. 1031.
    Zyryanov VN (1981) A contribution to the theory of Taylor columns in a stratified ocean. Izv Atmos Ocean Phys 17(10):793–800Google Scholar
  1032. 1032.
    Zyryanov VN (1985) Theory of steady ocean currents. Gydrometeoizdat, Lenigrad, 248 pp (in Russian)Google Scholar
  1033. 1033.
    Zyryanov VN (1986) Meandering flow past bottom relief. Izv Atmos Ocean Phys 22(12):1009–1014Google Scholar
  1034. 1034.
    Zyryanov VN (1995) Topographic eddies in sea currents dynamics. WPI RAS, Moscow, 240 pp (in Russian)Google Scholar
  1035. 1035.
    Zyryanov VN (2003) Topographic vortices in a stratified ocean. In: Borisov AV, Mamaev IS, Sokolovskiy MA (eds) Fundamental and applied problems of the vortex theory. Institute of Computer Science, Moscow–Izhevsk, pp 623–673 (in Russian)Google Scholar
  1036. 1036.
    Zyryanov VN (2006) Topographic eddies in a stratified ocean. Regul Chaotic Dyn 11(4):491–521Google Scholar
  1037. 1037.
    Zyryanov VN (2009) Secondary toroidal Taylor vortices above bottom perturbations in a rotating fluid. Dokl Phys 54(7):338–344Google Scholar
  1038. 1038.
    Zyryanov VN (2011) Secondary toroidal vortices above seamounts. J Mar Res 69(2–3):463–481Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Mikhail A. Sokolovskiy
    • 1
  • Jacques Verron
    • 2
  1. 1.RAS, Water Problems InstituteMoscowRussia
  2. 2.CNRSGrenobleFrance

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