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Modern Concepts About Oceanic Internal Waves

Chapter

Abstract

This chapter describes the modern concepts about oceanic internal waves. It presents the mathematical formulation of the internal motion in the ocean. Since the book is mainly the result of the experimental analysis of oceanic measurements the processing tools for the measurements of field data are presented here together with the description of the Vlasenko numerical model for the generation, propagation, and dissipation of internal tides. The Garrett and Munk spectral background model is also described because this is important for understanding the internal motion despite the fact that it does not describe internal tides. Mechanisms of internal tide generation are analyzed and general notes on internal wave motion are presented.

References

  1. Althaus AM, Kunze E, Sanford TB (2003) Internal tide radiation from Mendocino Escarpment. J Phys Oceanogr 33:1510–1527CrossRefGoogle Scholar
  2. Baines PG (1973) The generation of internal tides by flat-bump topography. Deep-Sea Res 20:179–205Google Scholar
  3. Baines PG (1974) The generation of internal tides over steep continental slopes. Phil Trans Roy Soc London Ser A 277:27–58CrossRefGoogle Scholar
  4. Baines PG (1982) On internal tide generation models. Deep-Sea Res 29(3):307–338CrossRefGoogle Scholar
  5. Barbee WB, Dworski JG, Irish JB, Larsen LN, Rattray M (1975) Measurements of internal waves of tidal frequency near a continental boundary. J Geophys Res 80(15):1965–1974CrossRefGoogle Scholar
  6. Barber NF (1963) The directional resolving power of an array of wave detectors. In: Ocean wave spectra. Prentice Hall, Engelwood Cliffs, NJ, pp 137–150Google Scholar
  7. Bell TH (1975) Topographically generated internal waves in the open ocean. J Geophys Res 80(3):320–327CrossRefGoogle Scholar
  8. Bell TH (1976) The structure of internal wave spectra as determined from towed thermistor chain measurements. J Geophys Res 81(21):3709–3714CrossRefGoogle Scholar
  9. Belyayev VS, Gezentsvey AN (1978) Shear instability of internal waves in the ocean, Izv. Acad. Sci. USSR, Ser. Atmosph Oceanic Phys 14(6):459–463Google Scholar
  10. Benilov AY, Solntseva NI, Filyushkin BN (1978) Relationship between the variability of the wind field and internal waves. Oceanology 18(3):257–266Google Scholar
  11. Blackford BL (1978) On the generation of internal waves by tidal flow over a sill—a possible nonlinear mechanism. J Mar Res 36(3):529–549Google Scholar
  12. Blackman RB, Tukey JW (1958) The measurements of power spectra from the point of view of communications engineering. Dover, NYGoogle Scholar
  13. Bogdanov KT, Sebekin BI (1976) Generation of internal tides and the influence of Earth’s tides on tidal motions in the ocean, Izv. Acad. Sci. USSR, Ser. Atmosph Oceanic Phys 12(5):326–329Google Scholar
  14. Bolshakov VN, Sabinin KD (1983) Mean characteristics of semidiurnal tidal currents in Polygon-70 and their variability. Izv. Acad. Sci. USSR, Ser. Atmosph Oceanic Phys. 19(1):51–56Google Scholar
  15. Borisenko YD (1975) Generation of internal waves in a two-layer fluid by a travelling pressure system. Izv. Acad. Sci. USSR, Ser. Atmosph Oceanic Phys 11(6):411–413Google Scholar
  16. Brekhovskikh LM, Goncharov VV, Kurtepov VM, Naugolnykh KA (1972) Resonant excitation of internal waves by nonlinear interaction of surface waves. Izv. Acad. Sci. USSR, Ser. Atmosph Oceanic Phys 11(6):411–413Google Scholar
  17. Brekhovskikh LM, Konjaev KV, Sabinin KD, Serikov AN (1975) Short-period internal waves in the sea. J Geophys Res 80(3):856–864CrossRefGoogle Scholar
  18. Brown ED, Owens B (1981) Observations of the horizontal interactions between the internal wave field and the mesoscale flow. J Phys Oceanogr 11(11):1474–1480CrossRefGoogle Scholar
  19. Bukatov AE, Kushnir VM, Smirnov GV (1978) Tidal-period internal waves in the equatorial zone of the Indian Ocean. Oceanology 18(5):514–519Google Scholar
  20. Cacchione DA, Pratson LF, Ogston AS (2002) The shaping of continental slopes by internal tides. Science 296:724–727CrossRefGoogle Scholar
  21. Cairns JL (1975) Internal wave measurements from a mid-water float. J Geophys Res 80(C3):299–306CrossRefGoogle Scholar
  22. Cairns JL, La Fond EC (1966) Periodic motions of the seasonal thermocline along the southern California coast. J Geophys Res 71(16):903–3916CrossRefGoogle Scholar
  23. Cairns JL, Williams GO (1976) Internal wave observations from a mid-water float. J Geophys Res 81(C12):1943–1950CrossRefGoogle Scholar
  24. Cartwright DE (1977) Oceanic tides. Rep Prog Phys 40:665–708Google Scholar
  25. Cherkesov LV (1976) Hydrodynamics of surface and internal waves. Naukova Dumka Publishers, Kiev, p 363 (in Russian)Google Scholar
  26. Chuang W-S, Wang D-P (1981) Effects of a density front on the generation and propagation of internal tides. J Phys Oceanogr 11(10):1357–1374CrossRefGoogle Scholar
  27. Cox CS, Sandström H (1962) Coupling of internal and surface waves in water of variable depth. J Oceanogr Soc Jpn 20th anniversary volume, 499–513Google Scholar
  28. Defant A (1932) Die Gezeiten und inheren Gezeiten-wellen des Atlantischen Ozeans. Wiss. Ergebn. Dt. Atlant. Exoed. “Meteor” 1925–1927. Bd. 7. H. 1. 313 sGoogle Scholar
  29. Desaubies YJF (1973) Internal waves near the turning point. Geophys Fluid Dyn 5(1):143–154CrossRefGoogle Scholar
  30. Desaubies YJF (1975) A linear theory of internal wave spectra and coherences near the Väisälä frequency. J Geophys Res 80:895–899CrossRefGoogle Scholar
  31. Desaubies YJF (1976) Analytical representation of internal wave spectra. J Phys Oceanogr 6(6):976–981CrossRefGoogle Scholar
  32. Dotsenko SF (1976) Non-stationary internal waves generated by periodical pressure forcing. Proc Marine Hydrophys Inst 2(73):48–60Google Scholar
  33. Dushaw BD (2006) Mode-1 internal tides in the western North Atlantic Ocean. Deep-Sea Res 53(3):449–473CrossRefGoogle Scholar
  34. Egbert GD (1997) Tidal data inversion: interpolation and inference. Prog Oceanogr 40:53–80CrossRefGoogle Scholar
  35. Egbert GD, Ray RD (2000) Significant dissipation of tidal energy in the deep ocean inferred from satellite altimeter data. Nature 405:775–778CrossRefGoogle Scholar
  36. Egbert GD, Ray RD (2001) Estimates of M2 tidal energy dissipation from TOPEX/Poseidon altimeter data. J Geophys Res 106:22475–22502Google Scholar
  37. Egbert GD, Ray RD (2003) Semidiurnal and diurnal tidal dissipation from TOPEX/Poseidon altimetry. Geophys Res Lett 30(17):1907.  https://doi.org/10.1029/2003GL017676 CrossRefGoogle Scholar
  38. Emery KO (1956) Deep standing internal waves in California basins. Limnol Oceanogr 1(1):35–41CrossRefGoogle Scholar
  39. Fedosenko VS, Cherkesov LV (1968) Internal waves generated by underwater earthquakes. Izv. Acad. Sci. USSR, Ser. Atmosph Oceanic Phys 4(11):1197–1203Google Scholar
  40. Fjelstad JE (1933) Interne Wellen. Geophys Publication, OsloGoogle Scholar
  41. Fofonoff NP (1969) Spectral characteristics of internal waves in the ocean. Deep-Sea Res 16(Suppl.):58–71Google Scholar
  42. Foux VR (1982) An introduction to the theory of wave motions in the ocean. Leningrad State University Publishing House, Leningrad, p 199 (in Russian)Google Scholar
  43. Frankignoul C (1976) Observed interaction between oceanic internal waves and mesoscale eddies. Deep-Sea Res 23(9):805–820Google Scholar
  44. Frankignoul C, Joyce TM (1979) On the internal wave variability during the internal wave experiment (IWEX). J Geophys Res 84(C2):769–776CrossRefGoogle Scholar
  45. Garrett C (1968) On the interaction between internal gravity waves and a shear flow. J Fluid Mech 34:711–720CrossRefGoogle Scholar
  46. Garrett C (2003) Internal tides and ocean mixing. Science 301:1858–1859Google Scholar
  47. Garrett C, Gerkema T (2007) On the body-force term in internal-tide generation. J Phys Oceanogr 37(8):2172–2175CrossRefGoogle Scholar
  48. Garrett C, Kunze E (2007) Internal tide generation in the deep ocean. Annual Rev Fluid Mech 39:57–87CrossRefGoogle Scholar
  49. Garrett CJR, Munk WH (1972a) Space-time scales of internal waves. Geophys Fluid Dyn 3(3):225–264Google Scholar
  50. Garrett C, Munk W (1972b) Oceanic mixing by breaking internal waves. Deep-Sea Res 19(12):823–832Google Scholar
  51. Garrett C, Munk W (1975) Space-time scales of internal waves: a progress report. J Geophys Res 80(3):291–297CrossRefGoogle Scholar
  52. Garrett C, Munk W (1979) Internal waves in the ocean. Ann Rev Fluid Mech 11:339–369CrossRefGoogle Scholar
  53. Gerkema T (2001) Internal and interfacial tides: beam scattering and local generation of solitary waves. J Marine Res 59:227–255CrossRefGoogle Scholar
  54. Golubev YN, Ivanov VF, Cherkesov LV (1979) Generation of internal tides by the interaction of a barotropic wave with an elevation of isopycnal surface. In: Surface and internal waves. Sebastopol, pp 195–203 (in Russian)Google Scholar
  55. Gould WJ, McKee WD (1973) Observations of the vertical structure of semidiurnal tidal currents in the Bay of Biscay. Nature 224:88–91CrossRefGoogle Scholar
  56. Gregg MC, Briscoe MG (1979) Internal waves, finestructure, microstructure, and mixing in the ocean. Rev Geophys Space Phys 17(7):1524–1547CrossRefGoogle Scholar
  57. Gulev SK, Bolshakov VN (1979) Study of internal tide field isotropy, Vestnik. MGU. Geogr Ser 5:8–11Google Scholar
  58. Halpern D (1971) Observations on short-period internal waves in Massachusetts Bay. J Mar Res 29(2):116–132Google Scholar
  59. Haury LR, Briscoe MG, Orr MH (1979) Tidally generated internal wave packets in Massachusetts Bay. Nature 278:312–317CrossRefGoogle Scholar
  60. Helland-Hansen B, Nansen F (1909) The Norwegian Sea. Rep Norw Fish Marine Invest 2(1/2):1–64Google Scholar
  61. Hendershott MC (1973) Inertial oscillations of tidal period. Prog Oceanogr 6:1–27CrossRefGoogle Scholar
  62. Hibiya T (1990) Generation mechanism of internal waves by a vertically sheared tidal flow over a sill. J Geophys Res 95:1757–1764.  https://doi.org/10.1029/JC095iC02p01757 CrossRefGoogle Scholar
  63. Hibiya T (2004) Internal wave generation by tidal flow over a continental shelf slope. J Oceanogr 60(3):637–643CrossRefGoogle Scholar
  64. Holloway PE (1987) Internal hydraulic jumps and solitons at a shelf break region on the Australian North West shelf. J Geophys Res 92(C5):5405–5416CrossRefGoogle Scholar
  65. Holloway PE (1996) A numerical model of internal tides with application to the Australian North West shelf. J Phys Oceanogr 26(1):21–37CrossRefGoogle Scholar
  66. Holloway PE, Merrifield MA (1999) Internal tide generation by seamounts, ridges, and islands. J Geophys Res 104(C11):25937–25951CrossRefGoogle Scholar
  67. Holloway PE, Pelinovsky EN, Talipova TG, Barnes B (1997) A nonlinear model of internal tide transformation on the Australian North West shelf. J Phys Oceanogr 27:871–896CrossRefGoogle Scholar
  68. Ivanov YA, Morozov EG (1983) Investigations of temperature fluctuations at tidal and inertial periods. In: Atlantic Hydrophysical Polygon-70. Amerind Co. Oxonian Press Ltd., New Delhi, pp 289–299Google Scholar
  69. Ivanov VA, Serebryany AN (1982) Frequency spectra of shortperiod internal waves in a nontidal sea. Izv. Acad. Sci. USSR, Ser. Atmosph Oceanic Phys 18(6):527–529Google Scholar
  70. Johnson WR, Sanford TB (1980) Anomalous behavior of internal gravity waves near Bermuda. J Phys Oceanogr 10(2):2021–2034CrossRefGoogle Scholar
  71. Johnston TMS, Merrifield MA (2003) Internal tide scattering at seamounts, ridges, and islands. J Geophys Res 108(C6):3180.  https://doi.org/10.1029/2002JC001528 CrossRefGoogle Scholar
  72. Johnston TMS, Merrifield MA, Holloway PE (2003) Internal tide scattering at the Line Islands Ridge. J Geophys Res 108(C11):3365.  https://doi.org/10.1029/2003JC001844 CrossRefGoogle Scholar
  73. Joyce TM (1974) Nonlinear interactions among standing surface and internal gravity waves. J Fluid Mech 63(4):801–825CrossRefGoogle Scholar
  74. Kantha LH, Tierney CC (1997) Global baroclinic tides. Prog Oceanog 40:163–178.  https://doi.org/10.1016/S0079-6611(97)00028-1 CrossRefGoogle Scholar
  75. Katsumata K, Hibiya T (2002) Internal wave generation by tidal flow over a sill in a rotating channel. J Geophys Res 107(C10):3176.  https://doi.org/10.1029/2001JC001096 CrossRefGoogle Scholar
  76. Katz EJ, Briscoe MG (1979) Vertical coherence of the internal wave field from towed sensors. J Phys Oceanogr 9(3):518–530CrossRefGoogle Scholar
  77. Kelly SM, Nash JD (2010) Internal-tide generation and destruction by shoaling internal tides. Geophys Res Lett 37:L23611.  https://doi.org/10.1029/2010GL045598 CrossRefGoogle Scholar
  78. Kelly SM, Nash JD, Kunze E (2010) Internal-tide energy over topography. J Geophys Res 115:C06014.  https://doi.org/10.1029/2009JC005618 CrossRefGoogle Scholar
  79. Khatiwala S (2003) Generation of internal tides in an ocean of finite depth: analytical and numerical calculations. Deep-Sea Res 50(1):3–21CrossRefGoogle Scholar
  80. Klymak JM, Gregg MC (2004) Tidally generated turbulence over the Knight Inlet sill. J Phys Oceanogr 34(5):1135–1151CrossRefGoogle Scholar
  81. Konyaev KV (1975a) An experimental study of short-period internal sea waves. Izv. Acad. Sci. USSR, Ser. Atmosph Oceanic Phys 11(3):170–176Google Scholar
  82. Konyaev KV, Sabinin KD (1973) New data on internal waves in the sea measured using distributed temperature sensors. Dokl Akad Nauk SSSR 209(1):86–89Google Scholar
  83. Konyaev KV, Sabinin KD (1992) Waves inside the ocean. Gidrometeoizdat, Saint Petersburg, p 272 (in Russian)Google Scholar
  84. Konyaev KV, Serebryany AN (1983) Internal waves in the shelf zone of the sea during a storm. Oceanology 23(4):421–423Google Scholar
  85. Krauss W (1966) Interne Wellen. Gebrüder Borntraeger, Berlin-NikolaseeGoogle Scholar
  86. Krauss W (1976) On currents, internal, and inertial waves in a stratified ocean due to variable winds. Dt Hyrdogr Ztschr 29(3):87–96Google Scholar
  87. Kunze E, Boss E (1998) A model for vortex-trapped internal waves. J Phys Oceanogr 28(10):2104–2115CrossRefGoogle Scholar
  88. Kushnir VM, Andryushchenko EG (1977) Nonstationary characteristics of short-period internal gravity waves in the ocean. Izv. Acad. Sci. USSR, Ser. Atmosph Oceanic Phys 13(11):844–845Google Scholar
  89. La Fond EC (1961) Isotherm follower. J Mar Res 19(1):33–39Google Scholar
  90. Lamb KG (1994) Numerical experiments of internal wave generation by strong tidal flow across a finite amplitude bank edge. J Geophys Res 99:843–864CrossRefGoogle Scholar
  91. St. Laurent LS, Garrett C (2002) The role of internal tides in mixing the deep ocean. J Phys Oceanogr 32(10):2882–2899Google Scholar
  92. LeBlond PH, Mysak LA (1978) Waves in the ocean. Elsevier oceanographic series. Elsevier, Amsterdam, p 602Google Scholar
  93. Lee WH, Cox CS (1966) Time variation of ocean temperature and its relation to internal waves and oceanic heat flow measurements. J Geophys Res 71(8):2101–2111CrossRefGoogle Scholar
  94. Legg S (2004a) Internal tides generated on a corrugated continental slope. Part I: cross-slope barotropic forcing. J Phys Oceanogr 34(1):156–173CrossRefGoogle Scholar
  95. Legg S (2004b) Internal tides generated on a corrugated continental slope. Part II: along-slope barotropic forcing. J Phys Oceanogr 34(8):1824–1838CrossRefGoogle Scholar
  96. Leonov AI, Miropolsky YZ (1973) Resonant excitation of internal gravity waves in the ocean by atmospheric pressure fluctuations. Izv. Acad. Sci. USSR, Ser. Atmosph Oceanic Phys 9(8):480–485Google Scholar
  97. Levine MD (1983) Internal waves in the ocean. Rev Geophys Space Phys 21(5):1206–1216CrossRefGoogle Scholar
  98. Lyashenko AF, Sabinin KD (1979) On the spatial structure of the internal tides on the 1970 hydrophysical test range in the Atlantic. Izv. Acad. Sci. USSR, Ser. Atmosph Oceanic Phys 15(8):595–601Google Scholar
  99. MacKinnon JA, Winters KB (2005) Subtropical catastrophe: significant loss of low-mode tidal energy at 28.9°. Geophys Res Lett 32(15):L15605.  https://doi.org/10.1029/2005GL023376 CrossRefGoogle Scholar
  100. Maeda A (1971) Phase velocity of semidiurnal internal waves at ocean weather station T. J Oceanogr Soc Jpn 27(4):163–174CrossRefGoogle Scholar
  101. Magaard L (1973) On the generation of internal gravity waves by a fluctuating buoyancy flux at the sea surface. Geophys Fluid Dyn 5(2):101–111CrossRefGoogle Scholar
  102. Magaard L (1974) On the generation of internal gravity waves by meteorological forces. Mem Soc Roy Sci Liege 6:79–84Google Scholar
  103. Magaard L, McKee WD (1973) Semidiurnal tidal current at “site D”. Deep-Sea Res 20(11):993–1010Google Scholar
  104. Makshtas AP, Sabinin KD (1972) Relation of the oscillations of sound scattering depth with internal waves in the ocean. Oceanology 12(4):746–749Google Scholar
  105. Martin S, Simmins W, Wunsch C (1972) The excitation of resonant triads by single internal wave. J Fluid Mech 53(1):17–44CrossRefGoogle Scholar
  106. Matsuura T, Hibiya T (1990) An experimental and numerical study of the internal wave generation by tide-topography interaction. J Phys Oceanogr 20(4):506–521CrossRefGoogle Scholar
  107. Matygin AS, Sabinin KD, Filonov AE (1982) Average spatial spectra of internal tides on the 1970 Atlantic hydrophysical test range. Izv. Acad. Sci. USSR, Ser. Atmosph Oceanic Phys 18(2):129–133Google Scholar
  108. Maxworthy T (1979) A note on the internal solitary waves produced by tidal flow over a three-dimensional ridge. J Geophys Res 84(C1):338–342CrossRefGoogle Scholar
  109. McComas CH, Müller P (1981) Time scales of resonant interactions among oceanic internal waves. J Phys Oceanogr 11(8):970–986CrossRefGoogle Scholar
  110. McEwan A (1971) Generation of resonantly excited standing internal gravity waves. J Fluid Mech 50(3):431–448CrossRefGoogle Scholar
  111. McPhee MG, Kantha LH (1989) Generation of internal waves by sea ice. J Geophys Res 94(C3):3287–3302CrossRefGoogle Scholar
  112. McPhee-Shaw E (2006) Boundary–interior exchange: reviewing the idea that internal-wave mixing enhances lateral dispersal near continental margins. Deep-Sea Res II 53(1–2):42–59CrossRefGoogle Scholar
  113. McWilliams JC (2016) Submesoscale currents in the ocean. Proc Roy Soc London A 472:20160117. http://dx.doi.org/10.1098/rspa.2016.0117. Last accessed Oct 2017
  114. Miles JW (1961) On the stability of a heterogeneous shear flow. J Fluid Mech 10(4):495–509CrossRefGoogle Scholar
  115. Miller G (1966) The flux of tidal energy out of the deep oceans. J Geophys Res 71(10):2485–2489CrossRefGoogle Scholar
  116. Miropolskiy YZ (1975b) Influence of shear flow on the generation of short-period internal waves in the ocean. Izv. Acad. Sci. USSR, Ser. Atmosph Oceanic Phys 11(9):585–589Google Scholar
  117. Miropolskiy YZ, Neiman VG (1974) Internal waves and temperature microstructure in the Timor Sea. Izv. Acad. Sci. USSR, Ser. Atmosph Oceanic Phys 10(11):730–736Google Scholar
  118. Miropolsky YZ (1975a) Generation of internal waves in the ocean by the wind field. Oceanology 15(5):519–532Google Scholar
  119. Miropolsky YZ (2001) Dynamics of internal gravity waves in the ocean. In: Shishkina O (ed) Springer, BerlinGoogle Scholar
  120. Mohri K, Hibiya T, Iwamae N (2010) Revisiting internal wave generation by tide-topography interaction. J Geophys Res 115:C11001.  https://doi.org/10.1029/2009JC005908 CrossRefGoogle Scholar
  121. Mork M (1968) On the formation of internal waves caused by tidal flow over a bottom irregularity. Rep Geophys Inst Univ, Bergen, Norway, p 28Google Scholar
  122. Morozov EG (1985) Oceanic internal waves. Nauka, Moscow, p 151 (in Russian)Google Scholar
  123. Morozov EG (1995) Semidiurnal internal wave global field. Deep-Sea Res 42(1):135–148CrossRefGoogle Scholar
  124. Morozov EG, Marchenko AV (2012) Short-period internal waves in an Arctic fjord (Spitsbergen). Izvestiya Atmos Ocean Phys 48(4):401–408.  https://doi.org/10.1134/S0001433812040123 CrossRefGoogle Scholar
  125. Morozov EG, Pelinovsky EN, Talipova TG (1998) Exceedance frequency for internal waves during the Mesopolygon-85 experiment in the Atlantic. Oceanology 38(4):521–527Google Scholar
  126. Morozov EG, Shchuka SA, Zapotyl’ko VS (2007) Towed spectra of internal waves in the pycnocline of the Baltic Sea. Dokl. Earth Sci 412(1):151–153.  https://doi.org/10.1134/S1028334X07010357 CrossRefGoogle Scholar
  127. Mowbray DE, Rarity BSH (1967) Theoretical and experimental investigation of the phase configuration of internal waves of small amplitude in a density stratified liquid. J Fluid Mech 28(1):1–16CrossRefGoogle Scholar
  128. Müller P (1976) On the diffusion of momentum and mass by internal gravity waves. J Fluid Mech 77(4):789–823CrossRefGoogle Scholar
  129. Müller P, Olbers DJ (1975) On the dynamics of internal waves in the deep ocean. J Geophys Res 80(27):3848–3860CrossRefGoogle Scholar
  130. Müller P, Olbers DJ, Willebrand J (1978) The IWEX spectrum. J Geophys Res 83(C1):479–500CrossRefGoogle Scholar
  131. Munk WH (1966) Abyssal recipes. Deep-Sea Res 13:207–230Google Scholar
  132. Munk WH (1980) Internal wave spectra at the buoyant and inertial frequencies. J Phys Oceanogr 10:1718–1728CrossRefGoogle Scholar
  133. Munk WH (1997) Once again: once again—tidal friction. Prog Oceanogr 40:7–35CrossRefGoogle Scholar
  134. Munk WH, Wunsch C (1998) Abyssal recipes II: energetics of tidal and wind mixing. Deep-Sea Res 45:1977–2010CrossRefGoogle Scholar
  135. Nansen F (1902) Oceanography of the North Pole basin: Norwegian North Pole expedition, 1893–1896. Scientific results. Longmans and Green, Toronto, pp 1–427Google Scholar
  136. Nash JD, Kunze E, Toole JM, Schmitt RW (2004) Internal tide reflection and turbulent mixing on the continental slope. J Phys Oceanogr 34(5):1117–1134CrossRefGoogle Scholar
  137. Navrotsky VV, Filyushkin BN (1969) Statistical analysis of time fluctuations of temperature in the surface layer of the sea. Izv. Acad. Sci. USSR, Ser. Atmosph Oceanic Phys 5(7):408–412Google Scholar
  138. Nesterov SV (1970) Resonance generation of internal waves. Izv. Acad. Sci. USSR, Ser. Atmosph Oceanic Phys 6(7):437–441Google Scholar
  139. New AL, da Silva JCB (2002) Remote-sensing evidence for the local generation of internal soliton packets in the central Bay of Biscay. Deep-Sea Res 49:915–934CrossRefGoogle Scholar
  140. Olbers DJ (1976) Nonlinear energy transfer and the energy balance of the internal wave field in the deep ocean. J Fluid Mech 74(2):375–398CrossRefGoogle Scholar
  141. Olbers DJ (1983) Models of the oceanic internal wave field. Rev Geophys Space Phys 21(7):1567–1606CrossRefGoogle Scholar
  142. Olbers D, Eden C (1990) Revisiting the generation of internal waves by resonant interaction with surface waves. J Phys Oceanogr 20(8):2335–2350Google Scholar
  143. Olbers DJ, Herterich K (1979) The spectral energy transfer from surface waves to internal waves in the ocean. J Fluid Mech 92(2):349–380CrossRefGoogle Scholar
  144. Olbers DJ, Pomphrey N (1981) Disqualifying two candidates for the energy balance of oceanic internal waves. J Phys Oceanogr 11(10):1423–1425CrossRefGoogle Scholar
  145. Orlanski I, Bryan K (1969) Formation of the thermocline step-structure by large amplitude internal gravity waves. J Geophys Res 74(28):6975–6983CrossRefGoogle Scholar
  146. Osborne AR, Burch TL (1980) Internal solitons in the Andaman Sea. Science 208(4443):451–459CrossRefGoogle Scholar
  147. Paoletti MS, Drake M, Swinney HL (2014) Internal tide generation in non-uniformly stratified deep oceans. J Geophys Res 119:1943–1956.  https://doi.org/10.1002/2013JC009469 CrossRefGoogle Scholar
  148. Perry RB, Schimke GR (1965) Large amplitude internal waves observed off the north-west coast of Sumatra. J Geophys Res 70(10):2319–2324CrossRefGoogle Scholar
  149. Pettersson O (1908) Strömstudier vid Őstersjönsportar. Sven Hydrogr Biol Komm Skr 3:13–37Google Scholar
  150. Phillips OM (1977) The dynamics of the Upper Ocean, 2nd edn. Cambridge University Press, NY, p 336Google Scholar
  151. Pinkel R (1975) Upper ocean internal wave observations. J Geophys Res 80(27):3892–3910CrossRefGoogle Scholar
  152. Polzin K (2004) Idealized solutions for the energy balance of the finescale internal wave field. J Phys Oceanogr 34:231–246CrossRefGoogle Scholar
  153. Polzin KL, Toole JM, Ledwell JR, Schmitt RW (1997) Spatial variability of turbulent mixing in the abyssal ocean. Science 276:93–96CrossRefGoogle Scholar
  154. Prinsenberg S, Rattray M (1975) Effects of continental slope and variable Brunt-Väisälä frequency on the coastal generation of internal tides. Deep-Sea Res 22:251–263Google Scholar
  155. Prinsenberg SJ, Wilmot WL, Rattray M (1974) Generation and dissipation of coastal internal tides. Deep-Sea Res 21(4):263–281Google Scholar
  156. Qian H, Shaw P-T, Ko DS (2010) Generation of internal waves by barotropic tidal flow over a steep ridge. Deep-Sea Res 57(12):1521–1531CrossRefGoogle Scholar
  157. Rattray M (1960) On the coastal generation of internal tides. Tellus 12:54–62CrossRefGoogle Scholar
  158. Rattray M, Dworsky J, Kovala P (1969) Generation of long internal waves at the continental slope. Deep-Sea Res 16(Suppl.):179–195Google Scholar
  159. Ray RD, Mitchum GT (1997) Surface manifestation of internal tides in deep ocean: observations from altimetry and island gauges. Prog Oceanogr 40:135–162CrossRefGoogle Scholar
  160. Regal R, Wunsch C (1973) M2-tidal currents in the western North Atlantic. Deep-Sea Res 20(5):493–502Google Scholar
  161. Reid JL (1956) Observations of internal tides in October 1950. Trans Am Geophys Union 37(3):15–20CrossRefGoogle Scholar
  162. Rhines P (1973) Observation of the energy containing ocean eddies and theoretical models of waves and turbulence. Boundary Layer Meteorol 4(10):345–360CrossRefGoogle Scholar
  163. Rippeth TP, Inall ME (2002) Observations of the internal tide and associated mixing across the Malin Shelf. J Geophys Res 107(C4):3028.  https://doi.org/10.1029/2000JC000761 CrossRefGoogle Scholar
  164. Rooth C, Düing W (1971) On the detection of inertial waves with pycnocline followers. J Phys Oceanogr 1(1):12–16CrossRefGoogle Scholar
  165. Roth MW, Briscoe MG, McComas CH (1981) Internal waves in the upper ocean. J Phys Oceanogr 11(9):1234–1247CrossRefGoogle Scholar
  166. Ruddick BR, Joyce TM (1979) Observations of interactions between the internal wave field and low frequency flows in the North Atlantic. J Phys Oceanogr 9(3):498–517CrossRefGoogle Scholar
  167. Rudnic P, Cochrane JD (1951) Diurnal fluctuations in bathythermograms. J Mar Res 3:257–261Google Scholar
  168. Sabinin KD (1973) Certain features of short-period internal waves in the ocean, Izv. Acad. Sci. USSR, Ser. Atmosph Oceanic Phys 9(1):32–36Google Scholar
  169. Sabinin KD (1982) High frequency internal wave spectra in the equatorial Indian Ocean. Oceanology 22(6):672–683Google Scholar
  170. Sabinin KD, Serebryany AN (2005) Intense internal waves in the ocean. J Mar Res 59:327–353.  https://doi.org/10.1357/002224001762842235 Google Scholar
  171. Sabinin KD, Serikov AN (1974) Results from the measurements of the space-time characteristics of short-period internal waves in the tropical Atlantic. Izv. Acad. Sci. USSR, Ser. Atmosph Oceanic Phys 10(10):650–657Google Scholar
  172. Sabinin KD, Shulepov VA (1981) Model of the frequency spectrum of internal waves in the ocean, Izv. Acad. Sci. USSR, Ser. Atmosph Oceanic Phys 17(1):48–54Google Scholar
  173. Sabinin KD, Shulepov VA, Filonov AE (1977) Spatial characteristics of tidal internal waves in the Iberian Basin. Izv. Acad. Sci. USSR, Ser. Atmosph Oceanic Phys 13(8):588–593Google Scholar
  174. Sabinin KD, Nazarov AA, Serikov AN (1987) Study of high amplitude internal waves near steep bottom rises, Izv. Acad. Sci. USSR, Ser. Atmosph Oceanic Phys 23(11):879–886Google Scholar
  175. Samelson RM (1998) Large-scale circulation with locally enhanced vertical mixing. J Phys Oceanogr 28:712–726CrossRefGoogle Scholar
  176. Samodurov AS (1982) Model of the climatic spectrum of internal waves in the ocean. Oceanology 22(2):130–133Google Scholar
  177. Sandström H, Elliott JA (1984) Internal tide and solitons on the Scotian Shelf: a nutrient pump at work. J Geophys Res 89(C4):6415–6426.  https://doi.org/10.1029/JC089iC04p06415 CrossRefGoogle Scholar
  178. Sawyer C (1983) Tidal phase of internal wave generation. J Geophys Res 88(4):2642–2648CrossRefGoogle Scholar
  179. Schott F (1971) On the horizontal coherence and internal wave propagation in the North Sea. Deep-Sea Res 18(3):291–308Google Scholar
  180. Schott F (1977) On the energetics of baroclinic tides in the North Atlantic. Ann Geophys 33:41–62Google Scholar
  181. Schott F, Willebrand J (1973) On the determination of internal wave directional spectra from moored instruments. J Mar Res 31(2):116–134Google Scholar
  182. Serebryaniy AN (1985) Internal waves in the coastal zone of a tidal sea. Oceanology 25(5):574–578Google Scholar
  183. Siedler G (1974) Observations of internal wave coherence in the deep ocean. Deep-Sea Res 21(8):597–610Google Scholar
  184. Sjöberg B, Stigebrandt A (1992) Computations of the geographical distribution of the energy flux to mixing process via internal tides and the associated vertical circulation in the ocean. Deep-Sea Res 39:269–291CrossRefGoogle Scholar
  185. Stevenson TN (1968) Some two-dimensional internal waves in a stratified fluid. J Fluid Mech 33(4):715–720CrossRefGoogle Scholar
  186. Sugiyama Y, Niwa Y, Hibiya T (2009) Numerically reproduced internal wave spectra in the deep ocean. Geophys Res Lett 36:L07601CrossRefGoogle Scholar
  187. Summers HJ, Emery KO (1963) Internal waves of tidal period off Southern California. J Geophys Res 68(3):827–840CrossRefGoogle Scholar
  188. Tareev BA (1965) Baroclinic internal waves induced during overflow of bottom irregularities and their influence on sedimentation in the ocean. Oceanology 5(1):45–52Google Scholar
  189. Tareev BA (1966) Dynamics of internal gravity waves in a continuously stratified ocean. Izv. Acad. Sci. USSR, Ser. Atmosph Oceanic Phys 2(10):1064–1075Google Scholar
  190. Thorpe SA (1966) On wave interactions in a stratified fluid. J Fluid Mech 24(4):737–751CrossRefGoogle Scholar
  191. Thorpe SA (1975) The excitation, dissipation, and interaction of internal waves in the deep ocean. J Geophys Res 80(3):328–338CrossRefGoogle Scholar
  192. Tomczak M (1967) Uber den Einfluss fluktulerender Windfelder auf ein stetig geschichtetes Meer. Dt Hydrogr Ztschr 20(3):101–129CrossRefGoogle Scholar
  193. Torgrimson GM, Hickey BM (1979) Barotropic and baroclinic tides over the continental slope and shelf off Oregon. J Phys Oceanogr 9:945–961CrossRefGoogle Scholar
  194. Turner JS (1973) Buoyancy effects in fluids. Cambridge, Cambridge University PressGoogle Scholar
  195. van Haren H (2005b) Internal waves near the buoyancy frequency in a narrow wave-guide. Deep-Sea Res 53:121–129Google Scholar
  196. Vlasenko VI (1992) Nonlinear model for the generation of baroclinic tides over extensive inhomogeneities of bottom topography. Phys Oceanogr (Morskoy gidrofizicheskiy zhurnal) 3:417–424Google Scholar
  197. Vlasenko VI, Morozov EG (1993) Generation of semidiurnal internal waves near a submarine ridge. Oceanology 33(3):282–286Google Scholar
  198. Vlasenko V, Stashchuk N, Hutter K (2002) Water exchange in fjords induced by tidally generated internal lee waves. Dyn Atmosph Oceans 35(1):63–83CrossRefGoogle Scholar
  199. Vlasenko V, Stashchuk N, Hutter K (2005) Baroclinic tides: theoretical modeling and observational evidence. Cambridge, Cambridge University Press, p 351Google Scholar
  200. Voit SS (1959) Waves at the interface between two fluids generated by a travelling pressure system. Proc Marine Hydrophysical Inst 17:33–40 [in Russian]Google Scholar
  201. Voorhis AD (1968) Measurements of vertical motion and partition of energy in the New England slope water. Deep-Sea Res 15(5):599–608Google Scholar
  202. Voronovich AG (1975) Resonance, three-wave interaction between internal waves. Oceanology 15(5):773–780Google Scholar
  203. Voronovich AG, Goncharov VV (1982) Influence of large-scale motions on the propagation of short internal waves. Izv. Acad. Sci. USSR, Ser. Atmosph Oceanic Phys 18(1):55–60Google Scholar
  204. Weston DE, Reay WW (1969) Tidal-period internal waves in a tidal stream. Deep-Sea Res 16(5):473–478Google Scholar
  205. Wunsch C (1975a) Deep ocean internal waves: what do we really know? J Geophys Res 80(3):339–343CrossRefGoogle Scholar
  206. Wunsch C (1975b) Internal tides in the ocean. Rev Geophys Space Phys 13(1):167–182CrossRefGoogle Scholar
  207. Wunsch C, Dahlen J (1974) A moored temperature and pressure recorder. Deep-Sea Res 21:145–154Google Scholar
  208. Wunsch C, Ferrari R (2004) Vertical mixing, energy, and the general circulation of the oceans. Ann Rev Fluid Mech 36:281–314.  https://doi.org/10.1146/annurev.fluid.36.050802.122121 CrossRefGoogle Scholar
  209. Wunsch C, Hendry R (1972) Array measurements of the bottom boundary layer and internal wave field on the continental slope. Geophys Fluid Dyn 4(2):101–145CrossRefGoogle Scholar
  210. Wunsch C, Webb S (1979) The climatology of deep ocean internal waves. J Phys Oceanogr 9(2):235–243CrossRefGoogle Scholar
  211. Zeilon N (1911) On tidal boundary waves and related hydrodynamical problems. Kgl sven vetenskapsakad handl 47(4):1–46Google Scholar
  212. Ziegenbein J (1969) Short internal waves in the Strait of Gibraltar. Deep-Sea Res 16(5):479–488Google Scholar
  213. Ziegenbein J (1970) Spatial observations of short internal waves in the Strait of Gibraltar. Deep-Sea Res 17(5):867–876Google Scholar

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© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Physical DepartmentShirshov Institute of Oceanology, Russian Academy of SciencesMoscowRussia

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