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.
Similar content being viewed by others
References
U. Frisch, Turbulence: the legacy of A.N. Kolmogorov (Cambridge Univ. Press, 1995)
R. Benzi, G. Paladin, S. Patarnello, P. Santangelo, A. Vulpiani, J. Phys. A 19, 3771 (1986)
R. Benzi, S. Patarnello, P. Santangelo, J. Phys. A 21, 1221 (1988)
J.C. McWilliams, J. Fluid Mech. 146, 21 (1984)
J.B. Weiss, J.C. McWilliams, Phys. Fluids A 5, 608 (1992)
C.F. Carnevale, J.C. McWilliams, Y. Pomeau, J.B. Weiss, W.R. Young, Phys. Rev. Lett. 66, 2735 (1991)
N.J. Zabusky, J.C. McWilliams, Phys. Fluids 25, 2175 (1982)
P.W.C. Vobseek, J.H.G.M. van Geffen, V.V. Meleshko, G.J.F. van Heijst, Phys. Fluids 9, 3315 (1997)
O.U. Velasco Fuentes, G.J.F. van Heijst, N.P.M. van Lipzig, J. Fluid Mech. 307, 11 (1996)
R. Benzi, M. Colella, M. Briscolini, P. Santangelo, Phys. Fluids A 4, 1036 (1992)
D.G. Dritschel, N.J. Zabusky, Phys. Fluids 8, 1252 (1996)
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
J.B. Weiss, A. Provenzale, J.C. McWilliams, Phys. Fluids 10, 1929 (1998)
L. Onsager, Nuovo Cimento, Suppl. 6, 279 (1949)
G. Joyce, D. Montgomery, J. Plasma Phys. 10, 107 (1973)
J. Fröhlich, D. Ruelle, Commun. Math. Phys. 87, 1 (1982)
E. Caglioti, P.L. Lions, C. Marchioro, M. Pulvirenti, Commun. Math. Phys. 143, 501 (1992)
R. Robert, J. Sommeria, Phys. Rev. Lett. 69, 2776 (1992)
F. Spineanu, M. Vlad, Phys. Rev. Lett. 95, 235003 (2005)
P.H. Chavanis, M. Lemou, Eur. Phys. J. B 59, 217 (2007)
J.L. Synge, Can. J. Math. 1, 257 (1949)
E.A. Novikov, Y.B. Sedov, Sov. Phys. JETP 22, 297 (1979)
X. Leoncini, L. Kuznetsov, G.M. Zaslavsky, Phys. Fluids 12, 1911 (2000)
E.A. Novikov, Sov. Phys. JETP 41, 937 (1975)
H. Aref, Phys. Fluids 22, 393 (1979)
H. Aref, Ann. Rev. Fluid Mech. 15, 345 (1983)
J. Tavantzis, L. Ting, Phys. Fluids 31, 1392 (1988)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
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
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjb/e2011-10775-0