Effect of viscosity in the dynamics of two point vortices: Exact results

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 63, Issue 5, 2001, Pages

  Agullo, Olivier ^a,b   Verga, Alberto ^a,c  

^a CNRS   (France)

^b Laboratoire MADIREL   (France)

^c CNRS ^*  (France)

Author keywords

[No Author keywords available]

Indexed keywords

BROWNIAN MOVEMENT; COMPRESSIBILITY OF LIQUIDS; GREEN'S FUNCTION; HAMILTONIANS; NAVIER STOKES EQUATIONS; PROBABILITY DENSITY FUNCTION; PROBABILITY DISTRIBUTIONS; VISCOSITY;

FOKKER-PLANCK EQUATION;

VORTEX FLOW;

EID: 0035335245     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.63.056304     Document Type: Article

References (29)

1. J. C. McWilliams, J. Fluid Mech. 146, 21 (1984).
2. G. F. Carnevale, J. C. McWilliams, Y. Pomeau, J. B. Weiss, and W. R. Young, Phys. Rev. Lett. 66, 2735 (1991).
3. J. B. Weiss and J. C. McWilliams, Phys. Fluids A 5, 608 (1993).
4. D. G. Dritshel and D. W. Waugh, Phys. Fluids A 4, 1737 (1992).
5. D. W. Waugh, Phys. Fluids A 4, 1745 (1992).
6. P. Saffman, Vortex Dynamics, Cambridge Monographs on Mechanics and Applied Mathematics (Cambridge University Press, Cambridge, 1995).
7. L. Ting and R. Klein, Viscous Vortical Flows (Springer-Verlag, Berlin, 1991).
8. T. S. Lundgren, Phys. Fluids, 25, 2193 (1982).
9. T. S. Lundgren, Phys. Fluids A 5, 1472 (1993).
10. H. K. Moffatt, in New Approaches and Concepts in Turbulence, edited by T. Dracos and A. Tsinober (Birkhäuser, Basel, 1993), pp. 121–129.
11. J. C. Vassilicos and J. G. Brasseur, Phys. Rev. E 54, 467 (1996).
12. J. R. Angilella and J. C. Vassilicos, Phys. Rev. E 59, 5427 (1999).
13. C. Marchioro and M. Pulvirenti, Commun. Math. Phys. 84, 483 (1982).
14. L. Kelvin, Proc. R. Soc. Edimburg VI, 94 (1867).
15. A. J. Chorin, J. Fluid Mech. 57, 785 (1973).
16. C. Marchioro and M. Pulvirenti, Mathematical Theory of Incompressible Nonviscous Fluids (Springer-Verlag, New York, 1994).
17. H. Lamb, Hydrodynamics (Cambridge University Press, Cambridge, 1932).
18. O. Agullo and A. D. Verga, Phys. Rev. Lett. 78, 2361 (1997).
19. E. Novikov, Zh. Eksp. Teor. Fiz. 68, 1868 (1975) [Sov. Phys. JETP 41, 937 (1975)].
20. H. Aref, Annu. Rev. Fluid Mech. 15, 345 (1983).
21. H. Helmholtz, Crelles 55, 25 (1858).
22. C. W. Gardiner, Handbook of Stochastic Methods (Springer-Verlag, Berlin, 1985).
23. J. Zinn-Justin, Quantum Field Theory and Critical Phenomena (Oxford, University Press, Oxford, 1989).
24. A. Verga (unpublished).
25. P. Meunier, T. Leweke, and M. Abid, in Advances in Turbulence VIII, edited by C. Dopazo (CIMNE, Barcelona, 2000), pp. 15–18.
26. I. I. Gihman and A. V. Skorohod, Stochastic Differential Equations (Springer-Verlag, Berlin, 1972).
27. I. Gradshteyn and I. Ryzhik, Table of Integrals, Series and Products (Academic Press, Boston, 1994).
28. H. Poincaré, Les Méthodes Nouvelles de la Mécanique Céleste (Gauthier-Villars, Paris, 1893), Chap. VIII, p. 1.
29. J. P. Ramis, Séries Divergentes et Théories Asymptotiques, Panoramas et Synthèses (Société Mathématique de France, Paris, 1992).