Passive tracer dynamics in 4 point-vortex flow

European Physical Journal B

Volumn 20, Issue 3, 2001, Pages 427-440

  Laforgia, A ^a   Leoncini, X ^b   Kuznetsov, L ^c   Zaslavsky, G M ^b,d  

^a UNIVERSITY OF FLORENCE   (Italy)

^b NEW YORK UNIVERSITY   (United States)

^c BROWN UNIVERSITY   (United States)

^d POLYTECHNIC UNIVERSITY   (United States)

Author keywords

05.45.Ac Low dimensional chaos

Indexed keywords

EID: 0001003292     PISSN: 14346028     EISSN: None     Source Type: Journal    
DOI: 10.1007/s100510170261     Document Type: Article

References (61)

1. H. Aref, J. Fluid Mech. 143, 1 (1984).
2. G.M. Zaslavsky, R.Z. Sagdeev, A.A. Chernikov, Zhurn. Eksp. Teor. Fiz. 94, 102 (1988) (Sov. Phys. JETP 67, 270 (1988).
3. G.M. Zaslavsky, R.Z. Sagdeev, A.A. Chernikov, Zhurn. Eksp. Teor. Fiz. 94, 102 (1988) (Sov. Phys. JETP 67, 270 (1988).
4. J. Ottino, The kinematics of Mixing: Stretching, Chaos, and Transport (Cambridge University Press, Cambridge, 1989).
5. H. Aref, Phil. Trans. R. Soc. London A 333, 273 (1990).
6. J. Ottino, Ann. Rev. Fluid Mech. 22, 207 (1990).
7. V. Rom-Kedar, A. Leonard, S. Wiggins, J. Fluid Mech. 214, 347 (1990).
8. G.M. Zaslavsky, R.Z. Sagdeev, D.A. Usikov, A.A. Chernikov, Weak Chaos and Quasiregular Patterns, (Cambridge Univ. Press, Cambridge, 1991).
9. A. Crisanti, M. Falcioni, G. Paladin, A. Vulpiani, Riv. Nuovo Cimento 14, 1 (1991).
10. A. Crisanti, M. Falcioni, A. Provenzale, P. Tanga, A. Vulpiani, Phys. Fluids A 4, 1805 (1992).
11. A. Provenzale, Annu. Rev. Fluid Mech. 31, 55 (1999).
12. A.J. Majda, J.P. Kramer, Phys. Rep. 314, 238 (1999).
13. J.B. Weiss, A. Provenzale, J.C. McWilliams, Phys. Fluids 10, 1929 (1998).
14. P. Tabeling, A.E. Hansen, J. Paret, in Chaos, Kinetics and Nonlinear Dynamics in Fluids and Plasma, edited by S. Benkadda, G. Zaslavsky, (Springer, 1998) p. 145.
15. A.E. Hansen, D. Marteau , P. Tabeling, Phys. Rev. E 58, 7261 (1998).
16. P. Tabeling, S. Burkhart, O. Cardoso, H. Willaime, Phys. Rev. Lett. 67, 3772 (1991).
17. V.V. Meleshko, M.Yu. Konstantinov, Vortex Dynamics and Chaotic Phenomena (World Scientific, Singapore, 1999).
18. R. Benzi, G. Paladin, S. Patarnello, P. Santangelo, A. Vulpiani, J. Phys. A 19, 3771 (1986).
19. R. Benzi, S. Patarnello, P. Santangelo, J. Phys. A 21, 1221 (1988).
20. J.B. Weiss, J.C. McWilliams, Phys. Fluids A 5, 608 (1992).
21. J.C. McWilliams, J. Fluid Mech. 146, 21 (1984).
22. J.C. McWilliams, J. Fluid Mech. 219, 361 (1990).
23. D. Elhmaïdi, A. Provenzale, A. Babiano, J. Fluid Mech. 257, 533 (1993).
24. G.F. Carnevale, J.C. McWilliams, Y. Pomeau, J.B. Weiss, W.R. Young, Phys. Rev. Lett. 66, 2735 (1991).
25. N.J. Zabusky, J.C. McWilliams, Phys. Fluids 25, 2175 (1982).
26. P.W.C. Vobseek, J.H.G.M. van Geffen, V.V. Meleshko, G.J.F. van Heijst, Phys. Fluids 9, 3315 (1997).
27. O.U. Velasco Fuentes, G.J.F. van Heijst, N.P.M. van Lipzig, J. Fluid Mech. 307, 11 (1996).
28. R. Benzi, M. Colella, M. Briscolini, P. Santangelo, Phys. Fluids A 4, 1036 (1992).
29. J.B. Weiss, in Semi-Analytic Methods for the Navier-Stokes Equations, CRM Proc. Lecture Notes, 20, 109, (1999).
30. D.G. Dritschel, N.J. Zabusky, Phys. Fluids 8, 1252 (1996).
31. A. Aref, in Trends in Mathematics, (Birkhäuser Verlag, 1999) p. 151.
32. C. Sire, P.H. Chavanis, Phys. Rev. E 61, 6644 (2000).
33. A.A. Chernikov, B.A. Petrovichev, A.V. Rogal'sky, R.Z. Sagdeev, G.M. Zaslavsky, Phys. Lett. A 144, 127 (1990).
34. T.H. Solomon, E.R. Weeks, H.L. Swinney, Physica D 76, 70 (1994).
35. E.R. Weeks, J.S. Urbach, H.L. Swinney, Physica D 97, 219 (1996).
36. G.M. Zaslavsky, D. Stevens, H. Weitzner, Phys. Rev E 48, 1683 (1993).
37. S. Kovalyov, Chaos 10, 153 (2000).
38. G. Haller, G. Yuan, Physica D 147, 352 (2000).
39. L. Kuznetsov, G.M. Zaslavsky, Phys. Rev E 58, 7330 (1998).
40. Z. Neufeld, T. Tél, J. Phys. A 30, 2263 (1997).
41. L. Kuznetsov, G.M. Zaslavsky, Phys. Rev. E. 61, 3777 (2000).
42. X. Leoncini, L. Kuznetsov, G.M. Zaslavsky, Phys. Rev. E 63, 036224 (2001).
43. H. Aref, Phys. Fluids 22, 393 (1979).
44. H. Aref, Ann. Rev. Fluid Mech. 15, 345 (1983).
45. E.A. Novikov, Sov. Phys. JETP 41, 937 (1975).
46. J.L. Synge, Can. J. Math. 1, 257 (1949).
47. X. Leoncini, L. Kuznetsov, G.M. Zaslavsky, Phys. Fluids 12, 1911 (2000).
48. J. Tavantzis, L. Ting, Phys. Fluids 31, 1392 (1988).
49. E.A. Novikov, Yu.B. Sedov, Sov. Phys. JETP 48, 440 (1978).
50. H. Aref, N. Pomphrey, Proc. R. Soc. Lond. A 380, 359 (1982).
51. S.L. Ziglin, Sov. Math. Dokl. 21, 296 (1980).
52. A. Babiano, G. Boffetta, A. Provenzale, A. Vulpiani, Phys. Fluids 6, 2465 (1994).
53. S. Boatto, R.T. Pierrehumbert, J. Fluid Mech. 394, 137 (1999).
54. H. Lamb, Hydrodynamics 6th edn. (New York, Dover, 1945).
55. D.I. Pullin, P.G. Saffman, Proc. R. Soc. Lond. A 432, 481 (1991).
56. R.I. McLachlan, P. Atela, Nonlinearity 5, 541 (1992).
57. G.M. Zaslavsky, M. Edelman, Chaos 10, 135 (2000).
58. V.K. Melnikov, in Transport, Chaos and Plasma Physics II, Proceedings, Marseille, edited by F. Doveil, S. Benkadda, Y. Elskens (World Scientific, Singapore, 1996), pp. 142-153.
59. V. Rom-Kedar, G.M. Zaslavsky, Chaos 9, 697 (1999).
60. G.M. Zaslavsky, M. Edelman, B.A. Niyazov, Chaos 7, 159 (1997).
61. V.V. Melezhko, M.Yu. Konstantinov, A.A. Gurzhi, T.P. Konovaljuk, Phys. Fluids A 4, 2779 (1992).