Streamline topologies for integrable vortex motion on a sphere

Physica D: Nonlinear Phenomena

Volumn 140, Issue 1-2, 2000, Pages 95-125

  Kidambi, Rangachari ^a   Newton, Paul K ^a  

^a University of Southern California ^*  (United States)

Author keywords

Bifurcation; Integrable systems; Point vortex; Streamline topologies

Indexed keywords

EID: 0346053689     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(99)00233-X     Document Type: Article

References (49)

1. A.A. Andronov, E.A. Leontovich, I.I. Gordon, A.G. Maier, Qualitative Theory of Second Order Dynamical Systems, Wiley, New York, 1973.
2. H. Aref, Motion of three vortices, Phys. Fluids 22 (3) (1979) 393-400.
3. H. Aref, Integrable, chaotic and turbulent vortex motion in two-dimensional flows, Ann. Rev. Fluid Mech. 15 (1983) 345-389.
4. H. Aref, M. Bröns, On stagnation points and streamline topology in vortex flows, J. Fluid Mech. 370 (1998) 1-27.
5. V.I. Arnold, B.A. Khesin, Topological Methods in Hydrodynamics, Springer, Berlin, AMS 125, 1998.
6. A.A. Bagrets, D.A. Bagrets, Nonintegrability of two problems in vortex dynamics, Chaos 7 (9) 1997.
7. V.A. Bogomolov, Dynamics of vorticity at a sphere, Fluid Dynamics (6) (1977) 863-870.
8. V.A. Bogomolov, Two dimensional fluid dynamics on a sphere, Izv. Atmos. Oc. Phys. 15 (1) (1979) 18-22.
9. J.Y.-K. Cho, L.M. Polvani, The emergence of jets and vortices in freely evolving, shallow-water turbulence on a sphere, Phys. Fluids 8 (6) (1996) 1531-1552.
10. U. Dallman, Topological structures of three-dimensional vortex flow separation, AIAA-83-1735, 1983.
11. P.J. Davis, The Schwarz Function and its Applications, Math. Assoc. of America, Washington, DC, 1974.
12. M. DiBattista, L. Polvani, Barotropic vortex pairs on a rotating sphere, J. Fluid Mech. 358 (1998) 107-133.
13. D.G. Dritschel, Vortex properties of 2D turbulence, Phys. Fluids A 5 (4) (1993) 984-997.
14. D.G. Dritschel, N.J. Zabusky, On the nature of vortex interactions and models in unforced nearly inviscid two-dimensional turbulence, Phys. Fluids A 8 (5) (1996) 1252-1256.
15. A.T. Fomenko, T.Z. Nguyen, Topological classification of integrable non-degenerate Hamiltonians on isoenergy three-dimensional spheres, in: A.T. Fomenko (Ed.), Advances in Soviet Math, Vol. 6, American Mathematical Society, Providence, RI, 1991, pp. 267-296.
16. A.T. Fomenko, Topological classification of all integrable Hamiltonian differential equations of general type with two degrees of freedom, in: T. Ratiu (Ed.), The Geometry of Hamiltonian Systems, Vol. 22, MSRI Publications, Springer, New York, 1991, pp. 131-340.
17. A. Gill, Atmosphere-Ocean Dynamics, International Geophysics Series, Vol. 30, Academic Press, New York, 1982.
18. R.W. Ghrist, P.J. Holmes, M.C. Sullivan, Knots and Links in Three-Dimensional Flows, Springer Lecture Notes in Mathematics, Vol. 1654, Springer, New York, 1997.
19. G. Haller, A.C. Poje, Finite time transport in aperiodic flows, Phys. D (3/4) (1998) 352-380.
20. D. Hally, Stability of streets of vortices on surfaces of revolution with a reflection symmetry, J. Math. Phys. 21 (1980) 211-217.
21. R. Kidambi, P.K. Newton, Motion of three point vortices on a sphere, Phys. D 116 (1998) 143-175.
22. R. Kidambi, P.K. Newton, Collapse of three vortices on a sphere, Nuovo Cimento, in press (2000).
23. R. Kidambi, P.K. Newton, Point vortex motion on a sphere with solid boundaries, Phys. Fluids, in press (2000).
24. Y. Kimura, H. Okamoto, Vortex motion on a sphere, J. Phys. Soc. Jpn. 56 (12) (1987) 4203-4206.
25. R.H. Kraichnan, Statistical dynamics of two-dimensional flows, J. Fluid Mech. 67 (1975) 155-175.
26. C.C. Lim, Relative equilibria of symmetric n-body problems on the sphere: Inverse and direct results, Commun. Pure Appl. Math. LI (1998) 341-371.
27. C.C. Lim, Equilibrium statistics for point vortices on a rotating sphere (Preprint, 1998).
28. C.C. Lim, J. Montaldi, M. Roberts, Relative equilibria of point vortices on the sphere (Preprint, 1999).
29. T.S. Lundgren, Y.B. Pointin, Statistical mechanics of two-dimensional vortices, J. Statist. Phys. 17 (1977) 323-355.
30. E. Meiburg, P.K. Newton, N. Raju, G. Ruetsch, Unsteady models for the nonlinear evolution of the mixing layer, Phys. Rev. E 52 (1995) 1639.
31. I. Mezic, P.K. Newton, Statistical mechanics of point vortex motion on a sphere, Bulletin of the APS, DFD, 1999.
32. J. Miller, Statistical mechanics of Euler equations in two dimensions, Phys. Rev. Lett. 65 (1990) 2137-2140.
33. J. Miller, P. Weichman, M.C. Cross, Statistical mechanics, Euler's equations, and Jupiter's red spot, Phys. Rev. A 45 (1992) 2328-2359.
34. H.K. Moffatt, The degree of knottedness of tangled vortex lines, J. Fluid Mech. 35 (1) (1969) 117-129.
35. T. Needham, Visual Complex Analysis, Clarendon Press, Oxford, 1997.
36. E.A. Novikov, Dynamics and statistics of a system of vortices, Soviet Phys. JETP 41 (1975) 937-943.
37. E.A. Novikov, Y. Sedov, Vortex collapse, Soviet Phys. JETP 50 (1979) 297-301.
38. S. Pekarsky, J. Marsden, Point vortices on a sphere: stability of relative equilibria, J. Math. Phys. 39 (1998) 5894-5907.
39. L. Perko, Differential Equations and Dynamical Systems, TAM 7, 2nd Edition, Springer, Berlin, 1996.
40. A.E. Perry, M.S. Chong, A description of eddying motions and flow patterns using critical point concepts, Ann. Rev. Fluid Mech. 19 (1987) 125-155.
41. L.M. Polvani, D.G. Dritschel, Wave and vortex dynamics on the surface of a sphere, J. Fluid Mech. 255 (1993) 35-64.
42. L.M. Polvani, X.J. Carton, The tripole: a new coherent vortex structure of incompressible two-dimensional flow, Geophys. Astrophys. Fluid Dynamics 51 (1989) 87-102.
43. R. Robert, A maximum-entropy principle for two-dimensional perfect fluid dynamics, J. Statist. Phys. 65 (1991) 531-553.
44. R. Robert, J. Sommeria, Statistical equilibrium states for two-dimensional flows, J. Fluid Mech. 229 (1991) 291-310.
45. P.G. Saffman, Vortex Dynamics, Cambridge University Press, Cambridge, 1992.
46. A.S. Schwarz, Topology for Physicists, Springer, Berlin, 1994.
47. J.L. Synge, On the motion of three vortices, Canad. J. Math. 1 (1949) 257-270.
48. V. Szebehely, Theory of Orbits, Academic Press, New York, 1967.
49. S. Yoden, M. Yamada, A numerical experiment on two-dimensional decaying turbulence on a rotating sphere, J. Atmos. Sci. 50 (1993) 631.