Statistical mechanics of two-dimensional and geophysical flows

Physics Reports

Volumn 515, Issue 5, 2012, Pages 227-295

  Bouchet, Freddy ^a   Venaille, Antoine ^b  

^a UNIVERSITÉ DE LYON   (France)

^b PRINCETON UNIVERSITY   (United States)

Author keywords

2D Euler equations; 2D turbulence; Geophysical turbulence; Great Red Spot; Jupiter's troposphere; Kinetic theory; Large scales of turbulent flows; Long range interactions; Ocean jets; Ocean rings; Quasi geostrophic equations; Statistical mechanics

Indexed keywords

EID: 84861341086     PISSN: 03701573     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physrep.2012.02.001     Document Type: Review

References (207)

1. http://www.whoi.edu/science/PO/people/pberloff/.
2. Abramov R.V., Majda A.J. Statistically relevant conserved quantities for truncated quasigeostrophic flow. Proceedings of the National Academy of Science 2003, 100:3841-3846.
3. Aluie H., Eyink G.L. Localness of energy cascade in hydrodynamic turbulence. II. Sharp spectral filter. Physics of Fluids 2009, 21(11):115108.
4. Aref H. 150 Years of vortex dynamics. Theoretical and Computational Fluid Dynamics 2010, 24:1-7.
5. Arnold V.I. On an a-priori estimate in the theory of hydrodynamic stability. Izvestiya Vysshikh Uchebnykh Zavedeniǐ Matematika; Engl. transl.: American Mathematical Society Translations 1966, 79(2):267-269.
6. Barnier B., Madec G., Penduff T., Molines J., Treguier A., Le Sommer J., Beckmann A., Biastoch A., Böning C., Dengg J., Derval C., Durand E., Gulev S., Remy E., Talandier C., Theetten S., Maltrud M., McClean J., de Cuevas B. Impact of partial steps and momentum advection schemes in a global ocean circulation model at eddy-permitting resolution. Ocean Dynamics 2006, 56:543-567.
7. Berloff P., Hogg A.M., Dewar W. The turbulent oscillator: a mechanism of low-frequency variability of the wind-driven ocean gyres. Journal of Physical Oceanography 2007, 37:2363.
8. Bernard D., Boffetta G., Celani A., Falkovich G. Conformal invariance in two-dimensional turbulence. Nature Physics 2006, 2:124-128.
9. Bernard D., Boffetta G., Celani A., Falkovich G. Inverse turbulent cascades and conformally invariant curves. Physical Review Letters 2007, 98(2):024501.
10. Binney J., Tremaine S. Galactic dynamics 1987, University Press, Princeton, NJ, Princeton, 747 p., 1987.
11. Biryuk A. On invariant measures of the 2D Euler equation. Journal of Statistical Physics 2006, 122:597-616.
12. Boucher C., Ellis R.S., Turkington B. Spatializing random measures: doubly indexed processes and the large deviation principle. Annals of Probability 1999, 27:297-324.
13. F. Bouchet, Mécanique statistique des écoulements géophysiques, Ph.D., Université Joseph Fourier-Grenoble, 2001.
14. F. Bouchet, Parameterization of two dimensionnal turbulence using an anisotropic maximum entropy principle, cond-mat/0305205.
15. Bouchet F. Simpler variational problems for statistical equilibria of the 2D Euler equation and other systems with long range interactions. Physica D Nonlinear Phenomena 2008, 237:1976-1981.
16. Bouchet F., Barré J. Classification of phase transitions and ensemble inequivalence, in systems with long range interactions. Journal of Statistical Physics 2005, 118:1073-1105.
17. Bouchet F., Barre J., Venaille A. Equilibrium and out of equilibrium phase transitions in systems with long range interactions and in 2D flows. American Institute of Physics Conference Series 2008, vol. 970:117-152. A. Campa, A. Giansanti, G. Morigi, F.S. Labini (Eds.).
18. F. Bouchet, P.H. Chavanis, J. Sommeria, Statistical mechanics of Jupiter's Great Red Spot in the shallow water model, Preprint (in preparation).
19. Bouchet F., Corvellec M. Invariant measures of the 2D Euler and Vlasov equations. Journal of Statistical Mechanics: Theory and Experiment 2010, 8:P08021.
20. Bouchet F., Dauxois T. Prediction of anomalous diffusion and algebraic relaxations for long-range interacting systems, using classical statistical mechanics. Physical Review E 2005, 72(4):045103.
21. F. Bouchet, T. Dumont, Emergence of the great red spot of jupiter from random initial conditions, cond-mat/0305206.
22. Bouchet F., Gupta S., Mukamel D. Thermodynamics and dynamics of systems with long-range interactions. Physica A 2010, 4389-4405.
23. Bouchet F., Morita H. Large time behavior and asymptotic stability of the 2D Euler and linearized Euler equations. Physica D Nonlinear Phenomena 2010, 239:948-966.
24. Bouchet F., Simonnet E. Random changes of flow topology in two-dimensional and geophysical turbulence. Physical Review Letters 2009, 102(9):094504.
25. Bouchet F., Sommeria J. Emergence of intense jets and Jupiter's Great Red Spot as maximum-entropy structures. Journal of Fluid Mechanics 2002, 464:165-207.
26. Brands H., Chavanis P.H., Pasmanter R., Sommeria J. Maximum entropy versus minimum enstrophy vortices. Physics of Fluids 1999, 11:3465-3477.
27. Brands H., Stulemeyer J., Pasmanter R.A., Schep T.J. A mean field prediction of the asymptotic state of decaying 2D turbulence. Physics of Fluids 1997, 9:2465-2467.
28. Bretherton F.P., Haidvogel D.B. Two-dimensional turbulence above topography. Journal of Fluid Mechanics 1976, 78:129-154.
29. Bricmont J., Kupiainen A., Lefevere R. Ergodicity of the 2D Navier-Stokes equations with random forcing. Communications in Mathematical Physics 2001, 224:65-81.
30. Briggs R.J., Daugherty J.D., Levy R.H. Role of landau damping in crossed-field electron beams and inviscid shear flow. Physics of Fluids 1970, 13:421-432.
31. Brown S.N., Stewartson K. On the algebraic decay of disturbances in a stratified linear shear flow. Journal of Fluid Mechanics 1980, 100:811-816.
32. Bruneau C.H., Kellay H. Experiments and direct numerical simulations of two-dimensional turbulence. Physical Review E 2005, 71(4):046305.
33. Caglioti E., Lions P.L., Marchioro C., Pulvirenti M. A special class of stationary flows for two-dimensional euler equations: a statistical mechanics description. Part II. Communications in Mathematical Physics 1995, 174:229-260.
34. Caglioti E., Maffei C. Time asymptotics for solutions of Vlasov Poisson equation in a circle. Journal of Statistical Physics 1998, 92(1):301-323.
35. Caglioti E., Rousset F. Quasi-stationary states for particle systems in the mean-field limit. Journal of Statistical Physics 2007, 129(2):241-263.
36. Callen H.B. Thermodynamics and an Introduction to Thermostatistics 1985, 2nd Edition.
37. Campa A., Dauxois T., Ruffo S. Statistical mechanics and dynamics of solvable models with long-range interactions. Physics Reports 2009, 480:57-159.
38. Dynamics and Thermodynamics of Systems with Long Range Interactions: Theory and Experiments. American Institute of Physics Conference Series, 2008 2008, vol. 970. A. Campa, A. Giansanti, G. Morigi, F.S. Labini (Eds.).
39. Capel H.W., Pasmanter R.A. Evolution of the vorticity-area density during the formation of coherent structures in two-dimensional flows. Physics of Fluids 2000, 12:2514-2521.
40. Carnevale G.F., Frederiksen J.S. Nonlinear stability and statistical mechanics of flow over topography. Journal of Fluid Mechanics 1987, 175:157-181.
41. Case K.M. Stability of inviscid plane Couette flow. Physics of Fluids 1960, 3:143-148.
42. Chavanis P.H. Quasilinear theory of the 2D Euler equation. Physical Review Letters 2000, 84:5512-5515.
43. Chavanis P.H. Statistical mechanis of two-dimensional vortices and stellar systems. Lecture Notes in Physics 2002, vol. 602:208-289. Springer-Verlag. T. Dauxois, S. Ruffo, E. Arimondo, M. Wilkens (Eds.).
44. Chavanis P.H. Phase transitions in self-gravitating systems. International Journal of Modern Physics B 2006, 20:3113-3198.
45. Chavanis P.H. Dynamical and thermodynamical stability of two-dimensional flows: variational principles and relaxation equations. European Physical Journal B 2009, 70:73-105.
46. Chavanis P.H., Naso A., Dubrulle B. Relaxation equations for two-dimensional turbulent flows with a prior vorticity distribution. European Physical Journal B 2010, 77:167-186.
47. Chavanis P.H., Sommeria J. Classification of self-organized vortices in two-dimensional turbulence: the case of a bounded domain. Journal of Fluid Mechanics 1996, 314:267-297.
48. Chavanis P.H., Sommeria J. Thermodynamical approach for small-scale parametrization in 2D turbulence. Physical Review Letters 1997, 78:3302-3305.
49. Chavanis P.H., Sommeria J. Classification of robust isolated vortices in two-dimensional hydrodynamics. Journal of Fluid Mechanics 1998, 356:259-296.
50. Chavanis P.H., Sommeria J. Statistical mechanics of the shallow water system. Physical Review E 2002, 65(2):026302.
51. Chavanis P.H., Sommeria J., Robert R. Statistical mechanics of two-dimensional vortices and collisionless stellar systems. Astrophysical Journal 1996, 471:385.
52. Chelton D.B., Schlax M.G., Samelson R.M., de Szoeke R.A. Global observations of large oceanic eddies. Geophysical Research Letters 2007, 34:15606.
53. Chen P., Cross M.C. Phase diagram for coherent vortex formation in the two-dimensional inviscid fluid in circular geometries. Physical Review E 1994, 50:2022-2029.
54. Chen P., Cross M.C. Mean field equilibria of single coherent vortices. Physical Review E 1996, 54:6356-6363.
55. Chen P., Cross M.C. Mixing and thermal equilibrium in the dynamical relaxation of a vortex ring. Physical Review Letters 1996, 77:4174-4177.
56. Chertkov M., Connaughton C., Kolokolov I., Lebedev V. Dynamics of energy condensation in two-dimensional turbulence. Physical Review Letters 2007, 99:084501.
57. Clercx H.J.H., Maassen S.R., van Heijst G.J.F. Decaying two-dimensional turbulence in square containers with no-slip or stress-free boundaries. Physics of Fluids 1999, 11:611-626.
58. Danilov S., Gurarie D. Nonuniversal features of forced two-dimensional turbulence in the energy range. Physical Review E 2001, 63(2):020203.
59. Dauxois T., Ruffo S., Arimondo E., Wilkens M. Dynamics and Thermodynamics of Systems with Long-Range Interactions. Lecture Notes in Physics 2002, vol. 602. Springer Verlag, Berlin.
60. Dibattista M.T., Majda A.J. An equilibrium statistical theory for large-scale features of open-ocean convection. Journal of Physical Oceanography 2000, 30:1325-1353.
61. Dibattista M.T., Majda A.J., Marshall J. A statistical theory for the patchiness of open-ocean deep convection: the effect of preconditioning. Journal of Physical Oceanography 2002, 32:599-626.
62. Dowling T.E. Dynamics of Jovian atmospheres. Annual Review of Fluid Mechanics 1995, 27:293-334.
63. Dowling T.E., Ingersoll A.P. Potential vorticity and layer thickness variations in the flow around Jupiter's Great Red SPOT and White Oval BC. Journal of Atmospheric Sciences 1988, 45:1380-1396.
64. Drazin P.G., Reid W.H. Hydrodynamic stability 2004, Cambridge University Press. second edition.
65. Dritschel D.G., McIntyre M.E. Multiple jets as PV staircases: the Phillips effect and the resilience of Eddy-transport barriers. Journal of Atmospheric Sciences 2008, 65:855.
66. Dubin D.H.E., O'Neil T.M. Two-dimensional guiding-center transport of a pure electron plasma. Physical Review Letters 1988, 60(13):1286-1289.
67. Dubinkina S., Frank J. Statistical relevance of vorticity conservation in the Hamiltonian particle-mesh method. Journal of Computational Physics 2010, 229:2634-2648.
68. Dubrulle B., Nazarenko S. Interaction of turbulence and large-scale vortices in incompressible 2D fluids. Physica D 1997, 110:123-138.
69. Ellis R.S., Haven K., Turkington B. Large deviation principles and complete equivalence and nonequivalence results for pure and mixed ensembles. Journal of Statistical Physics 2000, 101:999.
70. Ellis R.S., Haven K., Turkington B. Nonequivalent statistical equilibrium ensembles and refined stability theorems for most probable flows. Nonlinearity 2002, 15:239-255.
71. Ellis R.S., Jordan R., Otto P., Turkington B. A statistical approach to the asymptotic behavior of a class of generalized nonlinear Schrödinger equations. Communications in Mathematical Physics 2004, 244:187-208.
72. Esler J.G. The turbulent equilibration of an unstable baroclinic jet. Journal of Fluid Mechanics 2008, 599:241-268.
73. Eyink G.L. Locality of turbulent cascades. Physica D Nonlinear Phenomena 2005, 207:91-116.
74. Eyink G.L., Aluie H. Localness of energy cascade in hydrodynamic turbulence. I. Smooth coarse graining. Physics of Fluids 2009, 21(11):115107.
75. Eyink G.L., Spohn H. Negative-temperature states and large-scale, long-lived vortices in two-dimensional turbulence. Journal of Statistical Physics 1993, 70:833-886.
76. Eyink G.L., Sreenivasan K.R. Onsager and the theory of hydrodynamic turbulence. Reviews of Modern Physics 2006, 78:87-135.
77. Farrell B.F., Ioannou P.J. Structure and spacing of jets in barotropic turbulence. Journal of Atmospheric Sciences 2007, 64:3652.
78. Farrell B.F., Ioannou P.J. A theory of baroclinic turbulence. Journal of Atmospheric Sciences 2009, 66:2444.
79. Fjortoft R. On the changes in the spectral distribution of kinetic energy for two-dimensional nondivergent flow. Tellus 1953, 5:225-230.
80. Fofonoff N.P. Steady flow in a frictionless homogeneous ocean. Journal of Marine Research 1954, 13:254-262.
81. Frederiksen J.S. Nonlinear studies on the effects of topography on baroclinic zonal flows. Geophysical and Astrophysical Fluid Dynamics 1991, 59:57-82.
82. Frederiksen J.S., O'Kane T.J. Entropy, Closures and subgrid modeling. Entropy 2008, 10:635-683.
83. Frisch U. Turbulence, Turbulence, by Uriel Frisch 1996, Cambridge University Press, Cambridge, UK, p. 310.
84. Frisch U., Kurien S., Pandit R., Pauls W., Ray S.S., Wirth A., Zhu J.-Z. Hyperviscosity, galerkin truncation, and bottlenecks in turbulence. Physical Review Letters 2008, 101(14):144501.
85. Gill A.E. Atmosphere-Ocean Dynamics 1982.
86. Gill A.E., Green J.S.A., Simmons A. Energy partition in the large-scale ocean circulation and the production of mid-ocean eddies. Deep-Sea Research 1974, 21:499-528.
87. Goldstein S., Lebowitz J.L. On the (Boltzmann) entropy of non-equilibrium systems. Physica D 2004, 193:53.
88. Grote M.J., Majda A.J. Crude closure dynamics through large scale statistical theories. Physics of Fluids 1997, 9:3431-3442.
89. Grote M.J., Majda A.J. Crude closure for flow with topography through large-scale statistical theory. Nonlinearity 2000, 13:569-600.
90. Hallberg R., Gnanadesikan A. The role of eddies in determining the structure and response of the wind-driven southern hemisphere overturning: results from the modeling eddies in the southern ocean (MESO) project. Journal of Physical Oceanography 2006, 36:2232.
91. Held I.M., Larichev V.D. A scaling theory for horizontally homogeneous, baroclinically unstable flow on a beta plane. Journal of Atmospheric Sciences 1996, 53:946-952.
92. Hertel W., Thirring P. Soluble model for a system with negative specific heat. Annals of Physics 1971, 63:520-533.
93. N.G. Hogg, H.M. Stommel, The Heton, an Elementary Interaction Between Discrete Baroclinic Geostrophic Vortices, and Its Implications Concerning Eddy Heat-Flow, in: Royal Society of London Proceedings Series A, 1985, 397.
94. Holloway G. From classical to statistical ocean dynamics. Surveys in Geophysics 2004, 25:203-219.
95. Holm D.D., Marsden J.E., Ratiu T., Weinstein A. Nonlinear stability of fluid and plasma equilibria. Physics Reports 1985, 123:1-2.
96. Holm D.D., Marsden J.E., Ratiu T.S. The Euler-Poincare equations and semidirect products with applications to continuum theories 1998, in: eprint arXiv:chao-dyn/9801015, p. 1015.
97. Ingersoll A.P., Vasavada A.R. Dynamics of Jupiter's atmosphere. IAU Special Session 1998, 1:1042-1049.
98. Isichenko M.B. Nonlinear landau damping in collisionless plasma and inviscid fluid. Physical Review Letters 1997, 78:2369-2372.
99. Jin D.Z., Dubin D.H.E. Regional maximum entropy theory of vortex crystal formation. Physical Review Letters 1998, 80:4434-4437.
100. Jin D.Z., Dubin D.H.E. Characteristics of two-dimensional turbulence that self-organizes into vortex crystals. Physical Review Letters 2000, 84:1443-1446.
101. R. Jordan, C. Josserand, Self-organization in nonlinear wave turbulence, in: eprint , 1999, p. 5023. arxiv:chao-dyn/9905023.
102. R. Jordan, B. Turkington, Statistical mechanics of organized structures in two-dimensional magnetofluid turbulence, vol. 30, 1997, pp. 3629-3636.
103. Joyce G., Montgomery D. Negative temperature states for the two-dimensional guiding-centre plasma. Journal of Plasma Physics 1973, 10:107.
104. Jung S., Morrison P.J., Swinney H.L. Statistical mechanics of two-dimensional turbulence. Journal of Fluid Mechanics 2006, 554:433-456.
105. Jüttner B., Thess A., Sommeria J. On the symmetry of self-organized structures in two-dimensional turbulence. Physics of Fluids 1995, 7:2108-2110.
106. Kazantsev E., Sommeria J., Verron J. Subgrid-scale Eddy parameterization by statistical mechanics in a barotropic ocean model. Journal of Physical Oceanography 1998, 28:1017-1042.
107. Kellay H., Goldburg W.I. Two-dimensional turbulence: a review of some recent experiments. Reports on Progress in Physics 2002, 65:845-894.
108. Kiessling M. Statistical equilibrium dynamics. American Institute of Physics Conference Series 2008, vol. 970:91-108. A. Campa, A. Giansanti, G. Morigi, F.S. Labini (Eds.).
109. Kiessling M.K.H., Lebowitz J.L. The micro-canonical point vortex ensemble: beyond equivalence. Letters in Mathematical Physics 1997, 42(1):43-56.
110. Kossin J.P., Schubert W.H. Mesovortices, polygonal flow patterns, and rapid pressure falls in hurricane-like vortices. Journal of Atmospheric Sciences 2001, 58:2196-2209.
111. Kraichnan R.H. Inertial ranges in two-dimensional turbulence. Physics of Fluids 1967, 10:1417-1423.
112. Kraichnan R.H., Montgomery D. Two-dimensional turbulence. Reports on Progress in Physics 1980, 43:547-619.
113. Kuksin S., Penrose A family of balance relations for the two-dimensional Navier-Stokes equations with random forcing. Journal of Statistical Physics 2005, 118(3-4):437-449.
114. Kuksin S., Shirikyan A. Stochastic dissipative PDE's and Gibbs measures. Communications in Mathematical Physics 2000, 213:291-330.
115. Kuksin S.B. The Eulerian limit for 2D statistical hydrodynamics. Journal of Statistical Physics 2004, 115:469-492.
116. Landau L.D., Lifshitz E.M. Statistical Physics. Course of Theoretical Physics 1980, Vol. 5. Pergamon Press.
117. Lapeyre G., Held I.M. Diffusivity, kinetic energy dissipation, and Closure theories for the Poleward Eddy heat flux. Journal of Atmospheric Sciences 2003, 60:2907-2916.
118. Laval J., Dubrulle B., Nazarenko S. Dynamical modeling of sub-grid scales in 2D turbulence. Physica D Nonlinear Phenomena 2000, 142:231-253.
119. Lee On some statitical properties of hydrodynamical and magnetohydrodynamical fields. Applied Mathematics 1952, 10(69).
120. Leprovost N., Dubrulle B., Chavanis P.H. Thermodynamics of magnetohydrodynamic flows with axial symmetry. Physical Review E 2005, 71(3):036311.
121. Leprovost N., Dubrulle B., Chavanis P.H. Dynamics and thermodynamics of axisymmetric flows: theory. Physical Review E 2006, 73(4):046308.
122. Lifshitz E.M., Pitaevskii L.P. Physical Kinetics, Course of Theoretical Physics 1981, Pergamon Press, Oxford.
123. Lilly D.K. Numerical simulation studies of two-dimensional turbulence: I. Models of statistically steady turbulence. Geophysical and Astrophysical Fluid Dynamics 1972, 3:289-319.
124. Lim C.C. A long range spherical model and exact solutions of an energy enstrophy theory for two-dimensional turbulence. Physics of Fluids 2001, 13:1961-1973.
125. Lim C.C., Singh Mavi R. Phase transitions of barotropic flow coupled to a massive rotating sphere. Derivation of a fixed point equation by the Bragg method. Physica A Statistical Mechanics and its Applications 2007, 380:43-60.
126. Lundgren T.S. Strained spiral vortex model for turbulent fine structure. Physics of Fluids 1982, 25:2193-2203.
127. Lynden-Bell D., Wood R. The gravo-thermal catastrophe in isothermal spheres and the onset of red-giant structure for stellar systems. Monthly Notices of the Royal Astronomical Society 1968, 138:495.
128. Majda A.J., Wang X. Nonlinear Dynamics and Statistical Theories for Basic Geophysical Flows 2006, Cambridge University Press.
129. Majda A.J., Wang X. The emergence of large-scale coherent structure under small-scale random bombardments. Communications on Pure and Applied Mathematics 2006, 59(4):467-500.
130. Marcus P.S. Jupiter's Great Red SPOT and other vortices. Annual Review of Astronomy and Astrophysics 1993, 31:523-573.
131. Marston J.B., Conover E., Schneider T. Statistics of an unstable barotropic jet from a cumulant expansion. Journal of Atmospheric Sciences 2008, 65:1955.
132. Marteau D., Cardoso O., Tabeling P. Equilibrium states of two-dimensional turbulence: an experimental study. Physical Review E 1995, 51:5124-5127.
133. J.C. Mattingly, Y.G. Sinai, An elementary proof of the existence and uniqueness theorem for the Navier-Stokes equations, ArXiv Mathematics,. http://e-prints:math/9903042.
134. Merryfield W.J. Effects of stratification on quasi-geostrophic inviscid equilibria. Journal of Fluid Mechanics 1998, 354:345-356.
135. Merryfield W.J., Cummins P.F., Holloway G. Equilibrium statistical mechanics of barotropic flow over finite topography. Journal of Physical Oceanography 2001, 31:1880-1890.
136. Michel J., Robert R. Large deviations for young measures and statistical mechanics of infinite dimensional dynamical systems with conservation law. Communications in Mathematical Physics 1994, 159:195-215.
137. Michel J., Robert R. Statistical mechanical theory of the great red spot of Jupiter. Journal of Statistical Physics 1994, 77:645-666.
138. Miller J. Statistical mechanics of Euler equations in two dimensions. Physical Review Letters 1990, 65(17):2137-2140.
139. Miller J., Weichman P.B., Cross M.C. Statistical mechanics, Euler's equation, and Jupiter's red spot. Physical Review A 1992, 45:2328-2359.
140. Modica L. The gradient theory of phase transitions and the minimal interface criterion. Archive for Rational Mechanics and Analysis 1987, 98:123-142.
141. Monchaux R., Ravelet F., Dubrulle B., Chiffaudel A., Daviaud F. Properties of steady states in turbulent axisymmetric flows. Physical Review Letters 2006, 96(12):124502.
142. H. Morita, E. Simonnet, F. Bouchet, Statistical properties of out of equilibrium phase transitions for the 2D Navier-Stokes equations, Physical Review E (submitted for publication).
143. Morrison P.J. Hamiltonian description of the ideal fluid. Reviews of Modern Physics 1998, 70:467-521.
144. C. Mouhot, C. Villani, On the landau damping, arxiv:0904.2760.
145. A. Naso, P.H. Chavanis, B. Dubrulle, Statistical mechanics of Fofonoff flows in an oceanic basin, ArXiv http://e-prints:1007.0164.
146. Naso A., Chavanis P.H., Dubrulle B. Statistical mechanics of two-dimensional Euler flows and minimum enstrophy states. European Physical Journal B 2010, 77:187-212.
147. Naso A., Monchaux R., Chavanis P.H., Dubrulle B. Statistical mechanics of Beltrami flows in axisymmetric geometry: theory reexamined. Physical Review E 2010, 81(6):066318.
148. Nazarenko S. Exact solutions for near-wall turbulence theory. Physics Letters A 2000, 264:444-448.
149. Nazarenko S., Laval J.-P. Non-local two-dimensional turbulence and Batchelor's regime for passive scalars. Journal of Fluid Mechanics 2000, 408:301-321.
150. Nazarenko S., Quinn B. Triple cascade behavior in quasigeostrophic and drift turbulence and generation of zonal jets. Physical Review Letters 2009, 103(11):118501.
151. Nicholson D. Introduction to Plasma Theory 1983, Wiley, New-York.
152. Onsager L. Statistical hydrodynamics. Nuovo Cimento 1949, 6(No. 2 (Suppl.)):249-286.
153. Paret J., Jullien M., Tabeling P. Vorticity statistics in the two-dimensional enstrophy cascade. Physical Review Letters 1999, 83:3418-3421.
154. Paret J., Tabeling P. Intermittency in the two-dimensional inverse cascade of energy: experimental observations. Physics of Fluids 1998, 10:3126-3136.
155. J. Pedlosky, Geophysical fluid dynamics, 1982.
156. Pedlosky J. Ocean Circulation Theory 1998, Springer-Verlag, New York, Berlin.
157. Pego R.L., Weinstein M.I. Asymptotic stability of solitary waves. Communications in Mathematical Physics 1994, 164:305-349.
158. Pomeau Y. Statistical approach (to 2D turbulence). Turbulence: A Tentative Dictionary 1995, 117-123. Plenum Press, New York. P. Tabeling, O. Cardoso (Eds.).
159. Prieto R., Schubert W.H. Analytical predictions for zonally symmetric equilibrium states of the stratospheric polar vortex. Journal of Atmospheric Sciences 2001, 58:2709-2728.
160. Qiu B., Miao W. Kuroshio path variations south of Japan: bimodality as a self-sustained internal oscillation. Journal of Physical Oceanography 2000, 30:2124-2137.
161. Ritz W., Einstein A. Zum gegenwärtigen Stand des Strahlungsproblems. Physikalische Zeitschrift 1909, 10:323-324.
162. Robert R. Etats d'équilibre statistique pour l'écoulement bidimensionnel d'un fluide parfait. Comptes Rendus de l'Academie des Sciences 1 1990, 311:575-578.
163. Robert R. A maximum-entropy principle for two-dimensional perfect fluid dynamics. Journal of Statistical Physics 1991, 65:531-553.
164. Robert R. On the statistical mechanics of 2D Euler equation. Communications in Mathematical Physics 2000, 212:245-256.
165. Robert R., Rosier C. The modeling of small scales in two-dimensional turbulent flows: a statistical mechanics approach. Journal of Statistical Physics 1997, 86:481-515.
166. Robert R., Rosier C. Long range predictability of atmospheric flows. Nonlinear Processes in Geophysics 2001, 8:55-67.
167. Robert R., Sommeria J. Statistical equilibrium states for two-dimensional flows. Journal of Fluid Mechanics 1991, 229:291-310.
168. Robert R., Sommeria J. Relaxation towards a statistical equilibrium state in two-dimensional perfect fluid dynamics. Physical Review Letters 1992, 69(19):2776-2779.
169. Rosencrans S.I., Sattinger D.H. On the spectrum of an operator occuring in the theory of hydrodynamic stability. Journal of Mathematical Physics 1966, 45:289-300.
170. Salmon R. Lectures on Geophysical Fluid Dynamics 1998, Oxford University Press.
171. Salmon R., Holloway G., Hendershott M.C. The equilibrium statistical mechanics of simple quasi-geostrophic models. Journal of Fluid Mechanics 1976, 75:691-703.
172. Schecter D.A., Dubin D.H.E., Cass A.C., Driscoll C.F., Lansky I.M., O'Neil T.M. Inviscid damping of asymmetries on a two-dimensional vortex. Physics of Fluids 2000, 12:2397-2412.
173. Schecter D.A., Dubin D.H.E., Fine K.S., Driscoll C.F. Vortex crystals from 2D Euler flow: experiment and simulation. Physics of Fluids 1999, 11:905-914.
174. Schmeits M.J., Dijkstraa H.A. Bimodal behavior of the kuroshio and the gulf stream. Journal of Physical Oceanography 2001, 31:3425-3456.
175. E. Segre, S. Kida, Late states of incompressible 2D decaying vorticity fields, in: eprint , 1997, p. 9020. arxiv:chao-dyn/9709020.
176. Seychelles F., Amarouchene Y., Bessafi M., Kellay H. Thermal convection and emergence of isolated vortices in soap bubbles. Physical Review Letters 2008, 100(14):144501.
177. Smith R.A., O'Neil T.M. Nonaxisymmetric thermal equilibria of a cylindrically bounded guiding-center plasma or discrete vortex system. Physics of Fluids B 1990, 2:2961-2975.
178. Sommeria J. Experimental study of the two dimensional inverse energy cascade in a square box. Journal of Fluid Mechanics 1986, 170:139-168.
179. Sommeria J. Two-dimensional turbulence. Les Houches 2001, vol. 74:385-447. S. Berlin (Ed.).
180. Sommeria J., Nore C., Dumont T., Robert R. Statistical theory of the Great Red SPOT of Jupiter. Academie des Science Paris Comptes Rendus Serie B Sciences Physiques 1991, 312:999-1005.
181. Sommeria J., Staquet C., Robert R. Final equilibrium state of a two-dimensional shear layer. Journal of Fluid Mechanics 1991, 233:661-689.
182. Spitzer L. Dynamical Evolution of Globular Clusters 1991, Princeton University Press.
183. Spohn H. Large Scale Dynamics of Interacting Particles 2002, Springer, New-York.
184. Stammer D. Global characteristics of ocean variability estimated from regional TOPEX/POSEIDON altimeter measurements. Journal of Physical Oceanography 1997, 27:1743-1769.
185. Tabeling P. Two-dimensional turbulence: a physicist approach. Physics Reports 2002, 362:1-62.
186. Thess A., Sommeria J., Jüttner B. Inertial organization of a two-dimensional turbulent vortex street. Physics of Fluids 1994, 6:2417-2429.
187. Thompson A.F., Young W.R. Two-layer baroclinic Eddy heat fluxes: zonal flows and energy balance. Journal of Atmospheric Sciences 2007, 64:3214.
188. Thomson W. On the stability of steady and of periodic fluid motion. Philosophical Magazine 1887, 24:188-196.
189. Tian Y., Weeks E.R., Ide K., Urbach J.S., Baroud C.N., Ghil M., Swinney H.L. Experimental and numerical studies of an eastward jet over topography. Journal of Fluid Mechanics 2001, 438:129-157.
190. Turkington B. On steady vortex flow in two dimensions, I. Communications in Partial Differential Equations 1983, 8(9):999-1030.
191. Turkington B. On steady vortex flow in two dimensions, II. Communications in Partial Differential Equations 1983, 8(9):999-1030.
192. Turkington B., Majda A., Haven K., Dibattista M. Statistical equilibrium predictions of jets and spots on Jupiter. PNAS 2001, 98:12346-12350.
193. Turkington B., Whitaker N. Statistical equilibrium computations of coherent structures in turbulent shear layers. SIAM Journal on Scientific Computing 1996, 17(6):1414-1433.
194. G.K. Vallis, Atmospheric and Oceanic Fluid Dynamics, 2006.
195. Vallis G.K., Carnevale G.F., Young W.R. Extremal energy properties and construction of stable solutions of the Euler equations. Journal of Fluid Mechanics 1989, 207:133-152.
196. Venaille A., Bouchet F. Statistical ensemble inequivalence and bicritical points for two-dimensional flows and geophysical flows. Physical Review Letters 2009, 102(10):104501.
197. A. Venaille, F. Bouchet, Oceanic rings and jets as statistical equilibrium states, ArXiv http://e-prints:1011.2556.
198. A. Venaille, F. Bouchet, Solvable phase diagrams and ensemble inequivalence for two-dimensional and geophysical turbulent flows, ArXiv http://e-prints:1011.2309.
199. Wang J., Vallis G.K. Emergence of Fofonoff states in inviscid and viscous ocean circulation models. Journal of Marine Research 1994, 52:83-127.
200. Weeks E.R., Tian Y., Urbach J.S., Ide K., Swinney H.L., Ghil M. Transitions between blocked and zonal flows in a rotating annulus. Science 1997, 278:1598.
201. Weichman P.B. Equilibrium theory of coherent vortex and zonal jet formation in a system of nonlinear Rossby waves. Physical Review E 2006, 73(3):036313.
202. Weinan E., Mattingly J.C. Ergodicity for the Navier-Stokes equation with degenerate random forcing: finite-dimensional approximation. Communications on Pure and Applied Mathematics 2001, 54:1386-1402.
203. Whitaker N., Turkington B. Maximum entropy states for rotating vortex patches. Physics of Fluids 1994, 6:3963-3973.
204. Wolansky G., Ghil M. Nonlinear stability for saddle solutions of ideal flows and symmetry breaking. Communications in Mathematical Physics 1998, 193:713-736.
205. Yin Z., Montgomery D.C., Clercx H.J.H. Alternative statistical-mechanical descriptions of decaying two-dimensional turbulence in terms of "patches" and "points". Physics of Fluids 2003, 15:1937-1953.
206. Zeitlin V. Finite-mode analogs of 2D ideal hydrodynamics: coadjoint orbits and local canonical structure. Physica D Nonlinear Phenomena 1991, 49:353-362.
207. Zou J., Holloway G. Entropy maximization tendency in topographic turbulence. Journal of Fluid Mechanics 1994, 263:361-374.