Dynamical and thermodynamical stability of two-dimensional flows: Variational principles and relaxation equations

European Physical Journal B

Volumn 70, Issue 1, 2009, Pages 73-105

  Chavanis, P H ^a  

^a Lab de Physique Théorique   (France)

Author keywords

[No Author keywords available]

Indexed keywords

BOLTZMANN; FUNCTIONALS; INVISCID FLOWS; MEAN FIELD; NUMERICAL ALGORITHMS; OPTIMIZATION PROBLEMS; RELAXATION EQUATIONS; TWO-DIMENSIONAL FLOW; VARIATIONAL PRINCIPLES;

ALGORITHMS; EULER EQUATIONS; TWO DIMENSIONAL; VARIATIONAL TECHNIQUES;

NONLINEAR EQUATIONS;

EID: 77953759720     PISSN: 14346028     EISSN: 14346036     Source Type: Journal    
DOI: 10.1140/epjb/e2009-00196-1     Document Type: Article

References (88)

1. J. Pedlosky, Geophysical Fluid Dynamics (Springer, Berlin, 1987)
2. P. Tabeling, Phys. Rep. 362, 1 (2002)
3. H.J.H. Clercx, G.J.F. van Heijst, App. Mech. Rev. 62, 020802 (2009)
4. P.H. Chavanis, Statistical mechanics of two-dimensional vortices and stellar systems in: Dynamics and Thermodynamics of Systems with Long Range Interactions, edited by T. Dauxois, S. Ruffo, E. Arimondo, M. Wilkens, Lect. Notes in Phys. 602, Springer (2002); [cond-mat/0212223]
5. J. Miller, Phys. Rev. Lett. 65, 2137 (1990)
6. R. Robert, J. Sommeria, JFM 229, 291 (1991)
7. P.S. Marcus, Annu. Rev. Astron. Astrophys. 31, 523 (1993)
8. B. Turkington, A. Majda, K. Haven, M. Dibattista, Proc. Natl. Acad. Sci. 98, 12 346 (2001)
9. R. Ellis, K. Haven, B. Turkington, Nonlin. 15, 239 (2002)
10. F. Bouchet, J. Sommeria, JFM 464, 165 (2002)
11. P.H. Chavanis, J. Sommeria, Phys. Rev. E 65, 026302 (2002)
12. P.H. Chavanis, Physica D 200, 257 (2005)
13. D. Lynden-Bell, MNRAS 136, 101 (1967)
14. P.H. Chavanis, J. Sommeria, R. Robert, ApJ 471, 385 (1996)
15. P.H. Chavanis, in preparation
16. L. Kelvin, Phil. Mag. 23, 529 (1887)
17. V.I. Arnol'd, J. Maéc. 5, 29 (1966)
18. R. Ellis, K. Haven, B. Turkington, J. Stat. Phys. 101, 999 (2000)
19. F. Bouchet, J. Barraé, J. Stat. Phys. 118, 1073 (2005)
20. P.H. Chavanis, Int. J. Mod. Phys. B 22, 3113 (2006)
21. H. Brands, P.H. Chavanis, R. Pasmanter, J. Sommeria, Phys. Fluids 11, 3465 (1999)
22. P.H. Chavanis, Physica A 365, 102 (2006)
23. G. Kaniadakis, Physica A 296, 405 (2001)
24. P.H. Chavanis, Phys. Rev. E 68, 036108 (2003)
25. T.D. Frank, Nonlinear Fokker-Planck Equations: Fundamentals and Applications (Springer-Verlag, 2005)
26. P.H. Chavanis, Eur. Phys. J. B 62, 179 (2008)
27. P. Bartholomew, MNRAS 151, 333 (1971)
28. H. Kandrup, ApJ 370, 312 (1991)
29. D.D. Holm, J.E. Marsden, T. Ratiu, A. Weinstein, Phys. Rep. 123, 1 (1985)
30. V.A. Antonov, Astr. Zh. 37, 918 (1960)
31. (translated in: Sov. Astron. 4, 859 (1961))
32. G.K. Vallis, G.F. Carnevale, W.R. Young, JFM 207, 133 (1989)
33. V.I. Arnol'd, Izv. Vyssh. Ucheb. Zaved. Matem 54, 3 (1966)
34. (translated in: Am. Math. Soc. Transl. 79, 267 (1969))
35. D. Lynden-Bell, N. Sanitt, MNRAS 143, 167 (1969)
36. A.J. Mestel, JFM 200, 19 (1989)
37. A. Bray, Adv. Phys. 43, 357 (1994)
38. G. Wolansky, M. Ghil, Comm. Math. Phys. 193, 713 (1998)
39. F. Bouchet, Physica D 237, 1976 (2008)
40. P.H. Chavanis, C. Sire, Physica A 356, 419 (2005)
41. P.H. Chavanis, A&A 451, 109 (2006)
42. C. Tsallis, J. Stat. Phys. 52, 479 (1988)
43. J. Binney, S. Tremaine, Galactic Dynamics (Princeton Series in Astrophysics, 1987)
44. A.R. Plastino, A. Plastino, Phys. Lett. A 174, 384 (1993)
45. H. Poincaraé, Acta Math. 7, 259 (1885)
46. J. Katz, MNRAS 183, 765 (1978)
47. P.H. Chavanis, A&A 401, 15 (2003)
48. G. Kuz'min, Statistical mechanics of the organisation into two-dimensional coherent structures, in Structural Turbulence, edited by M.A. Goldshtik, Acad. Naouk CCCP Novosibirsk, Institute of Thermophysics, pp. 103-114
49. L. Onsager, Nuovo Cimento Suppl. 6, 279 (1949)
50. R. Robert, J. Sommeria, Phys. Rev. Lett. 69 2776 (1992)
51. P.H. Chavanis, J. Sommeria, Phys. Rev. Lett. 78, 3302 (1997)
52. P.H. Chavanis, Phys. Rev. Lett. 84, 5512 (2000)
53. A. Mikelic, R. Robert, SIAM J. Math. Anal. 29, 1238 (1998)
54. C. Rosier, L. Rosier, Applicable Analysis 75, 441 (2000)
55. C. Rosier, L. Rosier, Quart. Appl. Math. 61, 213 (2003)
56. R. Robert, C. Rosier, J. Stat. Phys. 86, 481 (1997)
57. E. Kazantsev, J. Sommeria, J. Verron, J. Phys. Oceano. 28, 1017 (1998)
58. P.H. Chavanis, Physica D 237, 1998 (2008)
59. P.H. Chavanis, AIP Conf. Proc. 970, 39 (2008)
60. A. Naso, P.H. Chavanis, B. Dubrulle, in preparation
61. J. Miller, P.B. Weichman, M.C. Cross, Phys. Rev. A 45, 2328 (1992)
62. S. Tremaine, M. Haénon, D. Lynden-Bell,MNRAS 219, 285 (1986)
63. P.H. Chavanis, Physica A 359, 177 (2006)
64. C.E. Leith, Phys. Fluids 27, 1388 (1984)
65. R.H. Kraichnan, D. Montgomery, Rep. Progr. Phys. 43, 547 (1980)
66. P.H. Chavanis, J. Sommeria, JFM 314, 267 (1996)
67. P.H. Chavanis, Ph.D. thesis, ENS Lyon, 1996
68. B.M. Boghosian, Phys. Rev. E 53, 4754 (1996)
69. G. Joyce, D. Montgomery, J. Plasma Phys. 10, 107 (1973)
70. T.S. Lundgren, Y.B. Pointin, J. Stat. Phys. 17, 323 (1977)
71. P.H. Chavanis, M. Lemou, Eur. Phys. J. B 59, 217 (2007)
72. P.H. Chavanis, Phys. Rev. E 64, 026309 (2001)
73. P.H. Chavanis, Physica A 387, 1123 (2008)
74. P.H. Chavanis, Physica A 387, 6917 (2008)
75. P.H. Chavanis, J. Sommeria, JFM 356, 259 (1998)
76. V. Latora, A. Rapisarda, C. Tsallis, Physica A 305, 129 (2002)
77. A. Taruya, M. Sakagami, Physica A 318, 387 (2003)
78. R. Silva, J.S. Alcaniz, Phys. Lett. A 313, 393 (2003)
79. D. Jiulin, Europhys. Lett. 67, 893 (2004)
80. M.P. Leubner, Nonlin. Processes Geophys. 15, 531 (2008)
81. A. Venaille, F. Bouchet, Phys. Rev. Lett. 102, 104501 (2009)
82. N. Leprovost, B. Dubrulle, P.H. Chavanis, Phys. Rev. E 73, 046308 (2006)
83. R. Jordan, B. Turkington, J. Stat. Phys. 87, 661 (1997)
84. N. Leprovost, B. Dubrulle, P.H. Chavanis, Phys. Rev. E 71, 036311 (2005)
85. M. Lemou, F. Mehats, P. Raphael, preprint
86. L. Rayleigh, Proc. London Math. Soc. 11, 57 (1880)
87. P.G. Drazin, W.H. Reid, Hydrodynamic stability (Cambridge University Press, 1981)
88. R. Fjortoft, Tellus 5, 225 (1953)