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Offsprings of a point vortex

  • Statistical and Nonlinear Physics
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Abstract

The distribution engendered by successive splitting of one point vortex are considered. The process of splitting a vortex in three using a reverse three-point vortex collapse course is analysed in great details and shown to be dissipative. A simple process of successive splitting is then defined and the resulting vorticity distribution and vortex populations are analysed.

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References

  1. U. Frisch, Turbulence: the legacy of A.N. Kolmogorov (Cambridge Univ. Press, 1995)

  2. R. Benzi, G. Paladin, S. Patarnello, P. Santangelo, A. Vulpiani, J. Phys. A 19, 3771 (1986)

    Article  ADS  MATH  Google Scholar 

  3. R. Benzi, S. Patarnello, P. Santangelo, J. Phys. A 21, 1221 (1988)

    Article  ADS  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

  5. J.B. Weiss, J.C. McWilliams, Phys. Fluids A 5, 608 (1992)

    Article  MathSciNet  ADS  Google Scholar 

  6. C.F. Carnevale, J.C. McWilliams, Y. Pomeau, J.B. Weiss, W.R. Young, Phys. Rev. Lett. 66, 2735 (1991)

    Article  ADS  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

  8. P.W.C. Vobseek, J.H.G.M. van Geffen, V.V. Meleshko, G.J.F. van Heijst, Phys. Fluids 9, 3315 (1997)

    Article  MathSciNet  ADS  Google Scholar 

  9. O.U. Velasco Fuentes, G.J.F. van Heijst, N.P.M. van Lipzig, J. Fluid Mech. 307, 11 (1996)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. R. Benzi, M. Colella, M. Briscolini, P. Santangelo, Phys. Fluids A 4, 1036 (1992)

    Article  ADS  MATH  Google Scholar 

  11. D.G. Dritschel, N.J. Zabusky, Phys. Fluids 8, 1252 (1996)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. H. Aref, Turbulent Statistical dynamics of a system of point vortice (Birkhäuser Verlag, 1999), p. 151, Trends in Mathematics, ISBN 978-3-7643-6150-1

  13. J.B. Weiss, A. Provenzale, J.C. McWilliams, Phys. Fluids 10, 1929 (1998)

    Article  MathSciNet  ADS  MATH  Google Scholar 

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

    MathSciNet  Google Scholar 

  15. G. Joyce, D. Montgomery, J. Plasma Phys. 10, 107 (1973)

    Article  ADS  Google Scholar 

  16. J. Fröhlich, D. Ruelle, Commun. Math. Phys. 87, 1 (1982)

    Article  ADS  MATH  Google Scholar 

  17. E. Caglioti, P.L. Lions, C. Marchioro, M. Pulvirenti, Commun. Math. Phys. 143, 501 (1992)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  18. R. Robert, J. Sommeria, Phys. Rev. Lett. 69, 2776 (1992)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  19. F. Spineanu, M. Vlad, Phys. Rev. Lett. 95, 235003 (2005)

    Article  ADS  Google Scholar 

  20. P.H. Chavanis, M. Lemou, Eur. Phys. J. B 59, 217 (2007)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. J.L. Synge, Can. J. Math. 1, 257 (1949)

    Article  MathSciNet  MATH  Google Scholar 

  22. E.A. Novikov, Y.B. Sedov, Sov. Phys. JETP 22, 297 (1979)

    ADS  Google Scholar 

  23. X. Leoncini, L. Kuznetsov, G.M. Zaslavsky, Phys. Fluids 12, 1911 (2000)

    Article  MathSciNet  ADS  Google Scholar 

  24. E.A. Novikov, Sov. Phys. JETP 41, 937 (1975)

    ADS  Google Scholar 

  25. H. Aref, Phys. Fluids 22, 393 (1979)

    Article  ADS  MATH  Google Scholar 

  26. H. Aref, Ann. Rev. Fluid Mech. 15, 345 (1983)

    Article  MathSciNet  ADS  Google Scholar 

  27. J. Tavantzis, L. Ting, Phys. Fluids 31, 1392 (1988)

    Article  MathSciNet  ADS  MATH  Google Scholar 

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Leoncini, X., Barrat, A., Josserand, C. et al. Offsprings of a point vortex. Eur. Phys. J. B 82, 173–178 (2011). https://doi.org/10.1140/epjb/e2011-10775-0

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  • DOI: https://doi.org/10.1140/epjb/e2011-10775-0

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