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Two-Dimensional Barotropic and Baroclinic Vortices

  • E. J. Hopfinger
Part of the International Centre for Mechanical Sciences book series (CISM, volume 329)

Abstract

In the atmosphere and the oceans and on other planets, coherent structures or vortices are easily identified. For this reason, the study of the stability of isolated vortices and the dynamics of the interaction of pairs, triades or more is of fundamental interest for refined models of the general circulation and of geostrophic turbulence. Processes of heat transfer and the dispersion of biochemical components are closely connected with coherent structures. Two dimensional vortex dynamics in barotropic fluid is also a key problem in free shear flows with or without rotation. In this case, the main question is connected with the stability of these vortices to three-dimensional disturbances.

Keywords

Potential Vorticity Core Radius Point Vortex Relative Vorticity Azimuthal Velocity 
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.

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References

  1. 1.
    Overman, E.A. and Zabusky, N.J.: Evolution and merger of isolated vortex structures, Phys. Fluids, 25 (1982), 1297.ADSCrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Dritschel, D.G.: The stability and energetics of co rotating uniform vortices, J. Huid Mech., 157 (1985), 95.ADSMATHGoogle Scholar
  3. 3.
    Capéran, P. and Maxworthy,T.:An experimental investigation of the coalescence of two dimensional finite-core vortices , (submitted Phys. Fluids, 1986)Google Scholar
  4. 4.
    Flierl, G. R. Instability of vortices, in: WHOI Rep. n° 85–36 (1985), 119.Google Scholar
  5. 5.
    Carton, X. J., Flierl, G.R. & Polvani, L.M.: The generation of tripoles from unstable axisymmetric isolated vortex structures. Europhys. Lett. 9, (1989), 339.ADSCrossRefGoogle Scholar
  6. 6.
    Kloosterziel, R.C. and van Heijst, GJ.F.: An experimental study of unstable barotropic vortices in a rotating fluid, J. Fluid Mech., 223 (1991), 1.ADSCrossRefGoogle Scholar
  7. 7.
    Dritschel, D.G. and Legras, B.: The elliptical model of two-dimensional vortex dynamics: part II: Disturbance equations . submitted to Phys Fluids A (1991).Google Scholar
  8. 8.
    Griffiths, R.W. and Hopfinger, E.J.: Coalescing of geostrophic vortices. J. Fluid Mech. 178 (1987), 73.ADSCrossRefGoogle Scholar
  9. 9.
    Polvani, L. M., Zabusky, N.J. & Flierl, G.R.: The two-layer geostrophic vortex dynamics, Part I: Upper layer V-states and merger. J. Fluid Mech. 205 (1989), 215.ADSCrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    Verron, J., Hopfinger, E.J. and McWilliams, J. C: Sensitivity to initial conditions in the merging of two-layer baroclinic vortices., Phys Fluids A, 2 (6), (1990), 886.ADSCrossRefGoogle Scholar
  11. 11.
    Polvani, L. M.: Two-layer geostrophic vortex dynamics . Part II: Alignment and two-layer V-states, J. Fluid Mech., 225 (1991), 241.ADSCrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    Griffiths, R.W. and Hopfinger, E. J.: Experiments with baroclinic vortex pairs in a rotating fluid, J. Fluid Mech., 173 (1986), 501.ADSCrossRefGoogle Scholar
  13. 13.
    Flierl, G. R.: On the stability of geostrophic vortices., J. Fluid Mech., 197 (1988), 349.ADSCrossRefMATHMathSciNetGoogle Scholar
  14. 14.
    Gent, P. R. and Mc Williams, J. C: The instability of circular vortices, Geophys. Astrophys. Fluid Dyn., 35 (1986), 209.ADSCrossRefMATHGoogle Scholar
  15. 15.
    Saffman, P. G. & Szeto, R.: Equilibrium states of a pair of equal uniform vortices, Phys. Fluids, 23 ( 1980), 2339.MathSciNetGoogle Scholar
  16. 16.
    Melander, M.V., Zabusky, N.J. and McWilliams, J. C.: Axisymmetrization and vorticity filamentation. J. Fluid Mech. 178 (1987), 137.ADSCrossRefMATHGoogle Scholar
  17. 17.
    Winant C. D. and Browand F.K.: Vortex pairing: a mechanism of turbulent mixing layer growth at moderate Reynolds number. J. Fluid Mech. 63, (1974), 237.ADSCrossRefGoogle Scholar
  18. 18.
    Carnevale, G.F., Kloosterziel, R.C. and van Heijst, G.J.F.: Propagation of barotropic vortices over topographyin a rotating tank. J. Fluid Mech.(1991).Google Scholar
  19. 19.
    Gryanik, V. M.: Dynamics of singular geostrophic vortices in a two-level model of the atmosphere or ocean, Izv. Akad. Nauk. USSR Atmos. Oceanic Phys. 19 (1983), 171.MathSciNetGoogle Scholar
  20. 20.
    Hogg, N.G. & Stommel, H.M.: The heton, an elementary interaction between discrete baroclinic geostrophic vortices and its implications concerning eddy heat flow, Proc. Roy. Soc. Lond., A 397 (1985), 1.ADSCrossRefMATHGoogle Scholar
  21. 21.
    Pedlosky, J.: Geophysical Fluid Dynamics, Springer Verlag, 1979CrossRefMATHGoogle Scholar
  22. 22.
    Pedlosky, J. : The instability of continuous heton clouds, J. Atmos. Sci. 42 (1985), 1477.ADSCrossRefGoogle Scholar
  23. 23.
    Helfrich, K.R. and Send, U.: Finite amplitude evolution of two-layer geostrophic vortices, J. Fluid Mech. 197 (1988), 331.ADSCrossRefMATHGoogle Scholar
  24. 24.
    Verron, J. and Hopfinger, E.J.: The enigmatic merger conditions of two-layer bafoclinic vortices. CRAS, 1313 S.II (1991), 737.Google Scholar

Copyright information

© Springer-Verlag Wien 1992

Authors and Affiliations

  • E. J. Hopfinger
    • 1
  1. 1.University J.F. and CNRSGrenoble CedexFrance

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