Dynamics of a passive tracer in a velocity field of four identical point vortices

Journal of Fluid Mechanics

Volumn 394, Issue , 1999, Pages 137-174

  Boatto, Stefanella ^a,b,d   Pierrehumbert, Raymond T ^c  

^a UNIVERSITY OF CHICAGO   (United States)

^b UNIVERSITY OF CHICAGO   (United States)

^c UNIVERSITY OF CHICAGO   (United States)

^d Institut de Mecanique Celeste et de Calcul des ephemerides   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000002044     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112099005492     Document Type: Article

References (42)

1. AREF, H. 1982 Point vortex motions with a center of symmetry. Phys. Fluids 25, 2183.
2. AREF, H. 1984 Stirring by chaotic advection. J. Fluid Mech. 143, 1-21.
3. AREF, H. & POMPHREY, N. 1982 Integrable and chaotic motions of four vortices. I. The case of identical vortices. Proc. R. Soc. Lond. A 380, 359-387.
4. ARNOLD, V. I. 1980 Mathematical Methods of Classical Mechanics. Springer.
5. BABIANO, A., BOFFETTA, G., PROVENZALE, A. & VULPIANI, A. 1994 Chaotic advection in point vortex models and two-dimensional turbulence. Phys. Fluids 6, 2465-2474.
6. BADII, R. & POLITI, A. 1987 Renyi dimensions from local expansion rates. Phys. Rev. A 35, 1288.
7. BETTIN, G., GALGANI, G., GIORGILLI, A. & STRELCYN, J. M. 1980 Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems; a method for computing all of them. Mechanica, March, 21.
8. BOATTO, S. 1996 Dynamics of a passive tracer in the velocity field of four identical point-vortices. PhD thesis, University of Chicago (June).
9. CARNEVALE, G. F., MCWILLIAMS, J. C., POMEAU, Y., WEISS, J. B. & YOUNG, W. R. 1991 Evolution of vortex statistics in two-dimensional turbulence. Phys. Rev. Lett. 66, 2735.
10. CARTWRIGHT, J. H. E. & PIRO, O. 1992 The dynamics of Runge-Kutta methods. Intl J. Bifurcation Chaos 2, 427-449.
11. CELLETTI, A. & FALCOLINI, C. 1988 A remark on the KAM theorem applied to a four-vortex system. J. Statist. Phys. 52, 471-477.
12. CELLETTI, A. & CHIERCHIA, L. 1987 Rigorous estimates for a computer-assisted KAM theory. J. Math. Phys. 28, 2078-2086.
13. CHERTKOV, M., FALKOVICH, G., KOLOKOLOV I. & LEBEDEV, V. 1995 Statistics of a passive scalar advected by a large-scale two-dimensional velocity field: Analytic solution. Phys. Rev. E 51, 5609-5627.
14. CHORIN, A. J. & MARSDEN, J. E. 1993 A Mathematical Introduction to Fluid Mechanics. Springer.
15. CRISANTI, A., FALCIONI, M., VULPIANI, A. & PALADIN, G. 1991 Lagrangian chaos: transport, mixing and diffusion in fluids. Rivista del Nuovo Cimento 14 (12), 1-79.
16. HAIRER, E., NØRSETT, S. P. & WARNER, G. 1996 Solving Ordinary Differential Equations. Springer.
17. HORITA, T., HATA, H., ISHIZAKI, R. & MORI, H. 1990 Long-time correlations and expansion-rate spectra of chaos in Hamiltonian systems. Prog. Theor. Phys. 83, 1065-1070.
18. KIRCHHOFF, G. R. 1876 Vorlesungen über mathematische. Physik. Mechanik, Leipzig, Teubner.
19. LICHTENBERG, A. J. & LIEBERMAN, A. M. 1992 Regular and Chaotic Dynamics. Springer.
20. MACKAY, R. S., MEISS, J. D. & PERCIVAL, I. C. 1987 Resonances in area-preserving maps. Physica 27D, 1.
21. MARSDEN, J. E. & SCHEURLE, J. 1995 Pattern evocation and geometric phases in mechanical systems with symmetry. Dyn. Stab. Systems 10, 315-338.
22. MATHER, J. N. 1984 Non-existence of invariant circles. Ergod. Theor. Dyn. Syst. 4, 301-309.
23. MCLACHLAN, R. I. & ATELA, P. 1992 The accuracy of symplectic integrators. Nonlinearity 5, 541-562.
24. MCWILLIAMS, J. C. 1984 The emergence of isolated coherent vortices in turbulent flow. J. Fluid Mech. 146, 21-43.
25. MONTROLL, E. & SCHLESINGER, M. 1984 In Non-Equilibrium Phenomena II: From Stochastics to Hydrodynamics (ed. J. Leibowitz & E. Montroll). North-Holland.
26. MORBIDELLI, A. & GUZZO, M. 1996 The Nekhoroshev theorem and the asteroid belt dynamical system. Celest. Mech. Dyn. Astron. 65, 107-136.
27. MUZZIO, F. J., SWANSON, P. D. & OTTINO, J. M. 1991 The statistics of stretching and stirring in chaotic flows. Phys. Fluids A 3 (5), 822-834.
28. NOVIKOV, E. A. 1976 Dynamics and statistics of a system of vortices. Sov. Phys. JETP 41, 937-943.
29. OSELEDEC, V. I. 1968 A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems. Trans. Moscow Math. Soc. 19, 197.
30. OTT, E. 1993 Chaos in Dynamical Systems. Cambridge University Press.
31. PERCIVAL, I. C. 1979 In Nonlinear Dynamics and Beam-Beam Interaction (ed. M. Month & J. C. Herrera). AIP Conference Proceedings no. 57, pp. 302. American Institute of Physics.
32. PIERREHUMBERT, R. T. 1991b Large-scale horizontal mixing in planetary atmospheres. Phys. Fluids A 3, 1250.
33. PIERREHUMBERT, R. T. & YANG, H. 1993 Global chaotic mixing on isentropic surfaces. J. Atmos. Sci. 50, 2462-2480.
34. PRESS, W. H., FLANNERY, B. P., TEUKOLSKY, S. A. & VETTERLING, W. T. 1992 Numerical Recipes. Cambridge University Press.
35. PULLIN, D. I. & SAFFMAN, P. G. 1991 Long-time symplectic integration: the example of four-vortex motion. Proc. R. Soc. Lond. A 432, 481-494.
36. ROM-KEDAR, V. 1993 The topological approximation method. In Transport Chaos & Plasma Physics, p. 1. IMT, Marseilles.
37. SANZ-SERNA, J. M. & CALVO, M. P. 1994 Numerical Hamiltonian Problems. Chapman & Hall.
38. SHRAIMAN, B. I. & SIGGIA, E. D. 1994 Lagrangian path integrals and fluctuations in random flow. Phys. Rev. E 49, 2912-2927.
39. SIMÓ, C. 1994 Averaging under fast quasi-periodic forcing. In Hamiltonian Mechanics (Toruń, 1993). NATO Adv. Sci. Inst. B: Phys., vol. 331, pp. 13-34.
40. SOMMERIA, J., MEYERS, S. D. & SWINNEY, H. L. 1988 Laboratory model of a planetary eastward jet. Nature 337, 58-61.
41. WIGGINS, S. 1991 Chaotic Transport in Dynamical Systems. Springer.
42. WIGGINS, S. & MALHOTRA, N. 1998 Geometric structures, lobe dynamics, and Lagrangian transport in flows with aperiodic time-dependence, with applications to Rossby wave flow. J. Nonlinear Sci. 8, 401-456.