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Dynamics of vortices and drift waves: a point vortex model

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Abstract

The complex interactions of localized vortices with waves are investigated using a model of point vortices in the presence of a transverse or longitudinal wave. This simple model shows a rich dynamical behavior including oscillations of a dipole, splitting and merging of two like-circulation vortices, and chaos. The analytical and numerical results of this model have been found to predict under certain conditions, the behavior of more complex systems, such as the vortices of the Charney-Hasegawa-Mima equation, where the presence of waves strongly affects the evolution of large coherent structures.

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References

  1. N.J. Zabusky, J.C. McWilliams, Phys. Fluids 25, 2175 (1982)

    Article  ADS  MATH  Google Scholar 

  2. A. Hasegawa, C.G. Maclennan, Y. Kodama, Phys. Fluids 22, 2122 (1979)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. V. Zeitlin, “Nonlinear Dynamics of Rotating Shallow Water: Methods and Advances”, in Advances in Nonlinear Science and Complexity (Elsevier Science, Amsterdam, 2007), Vol. 2

  4. A. Hasegawa, K. Mima, Phys. Rev. Lett. 39, 205 (1977)

    Article  ADS  Google Scholar 

  5. P.H. Diamond, S.I. Itoh, K. Itoh, T.S. Hahm, Plasma Phys. Control. Fusion 47, R35 (2005)

    Article  ADS  Google Scholar 

  6. J.M. Kosterlitz, J.D. Thouless, J. Phys. C 6, 1181 (1973)

    Article  ADS  Google Scholar 

  7. X. Leoncini, A. Verga, S. Ruffo, Phys. Rev. E 57, 6377 (1998)

    Article  ADS  Google Scholar 

  8. J.C. McWilliams, J. Fluid Mech. 146, 21 (1984)

    Article  ADS  MATH  Google Scholar 

  9. A. Provenzale, Annu. Rev. Fluid Mech. 31, 55 (1999)

    Article  MathSciNet  ADS  Google Scholar 

  10. A. Bracco, J.C. McWilliams, A. Provenzale, G. Morante, J.B. Weiss, Phys. Fluids 12, 2931 (2000)

    Article  ADS  Google Scholar 

  11. G. Reznik, Izv. Atmos. Ocean. Phys. 46, 784 (2010)

    Article  MATH  Google Scholar 

  12. F. Dupont, R.I. McLachlan, V. Zeitlin, Phys. Fluids 10, 3185 (1998)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. S.V. Annibaldi, G. Manfredi, R.O. Dendy, Phys. Plasmas 9, 791 (2002)

    Article  ADS  Google Scholar 

  14. X. Leoncini, O. Agullo, S. Benkadda, G.M. Zaslavsky, Phys. Rev. E 72, 026218 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  15. W. Horton, Phys. Rep. 192, 1 (1990)

    Article  ADS  Google Scholar 

  16. C. Ferro Fontán, A. Verga, Phys. Rev. E 52, 6717 (1995)

    Article  ADS  Google Scholar 

  17. W. Horton, Rev. Mod. Phys. 71, 735 (1999)

    Article  ADS  Google Scholar 

  18. W.H. Matthaeus, W.T. Stribling, D. Martinez, S. Oughton, D. Montgomery, Physica D 51, 531 (1991)

    Article  ADS  MATH  Google Scholar 

  19. L. Onsager, Nuovo Cimento, Suppl. 6, 279 (1949)

    Article  MathSciNet  Google Scholar 

  20. O. Agullo, A. Verga, Phys. Rev. E 69, 056318 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  21. F. Spineanu, M. Vlad, Phys. Plasmas 12, 112303 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  22. W. Horton, A. Hasegawa, Chaos 4, 227 (1994)

    Article  ADS  Google Scholar 

  23. J.G. Charney, Geofys. Publ. Oslo 17, 1 (1948)

    MathSciNet  Google Scholar 

  24. J. Pedlosky, Geophysical Fluid Dynamics (Springer, Berlin, 1986)

  25. M. Lessieur, Turbulence in fluids (Kluwer Academic, Dordrecht, 1990)

  26. E. Kim, P.H. Diamond, Phys. Rev. Lett. 88, 225002 (2002)

    Article  ADS  Google Scholar 

  27. F. Spineanu, M. Vlad, Phys. Rev. Lett. 94, 235003 (2005)

    Article  ADS  Google Scholar 

  28. G.M. Reznik, J. Fluid Mech. 240, 405 (1992)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  29. M. Makino, K. Kamimura, T. Taniuty, J. Phys. Soc. Jpn 50, 980 (1981)

    Article  ADS  Google Scholar 

  30. I.M. Lansky, T.M. O’Neil, D.A. Schecter, Phys. Rev. Lett. 79, 1479 (1997)

    Article  ADS  Google Scholar 

  31. E.N. Lorenz, Tellus 12, 364 (1960)

    Article  ADS  Google Scholar 

  32. J.G. Charney, J. Atmos. Sci. 28, 1087 (1971)

    Article  ADS  Google Scholar 

  33. O. Agullo, A.D. Verga, Phys. Rev. Lett. 78 2361 (1997)

    Article  ADS  Google Scholar 

  34. C. Sire, P.H. Chavanis, J. Sopik, Phys. Rev. E 84, 056317 (2011)

    Article  ADS  Google Scholar 

  35. M. Kono, W. Horton, Phys. Fluids B 3, 3255 (1991)

    Article  MathSciNet  ADS  Google Scholar 

  36. C. Marchioro, M. Pulvirenti, “Mathematical Theory of Uncompressible Nonviscous Fluids”, in AppliedMathematical Science(Springer-Verlag, New York, 1994), Vol. 96

  37. P.G. Saffman, Vortex Dynamics, Cambridge Monographs on Mechanics and Applied Mathematics (Cambridge University Press, Cambridge, 1995)

  38. G.M. Zaslavsky, The Physics of Chaos in Hamiltonian Systems, 2nd edn. (Imperial College Press, London, 2007)

  39. M. Paoletti, T. Solomon, Europhys. Lett. 69, 819 (2005)

    Article  ADS  Google Scholar 

  40. M. Paoletti, T. Solomon, Phys. Rev. E 72, 46204 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  41. P.H. Chavanis, Phys. Rev. E 58, R1199 (1998)

    Article  MathSciNet  ADS  Google Scholar 

  42. P.H. Chavanis, Phys. Rev. E 64, 026309 (2001)

    Article  ADS  Google Scholar 

  43. D.A. Schecter, D.H.E. Dubin, Phys. Fluids 13, 1704 (2001)

    Article  ADS  Google Scholar 

  44. Y. Kiwamoto, K. Ito, A. Sanpei, A. Mohri, Phys. Rev. Lett. 85, 3173 (2000)

    Article  ADS  Google Scholar 

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Correspondence to Xavier Leoncini.

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Leoncini, X., Verga, A. Dynamics of vortices and drift waves: a point vortex model. Eur. Phys. J. B 86, 95 (2013). https://doi.org/10.1140/epjb/e2013-30800-6

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