Dissipation, topography, and statistical theories for large-scale coherent structure

Communications on Pure and Applied Mathematics

Volumn 50, Issue 12, 1997, Pages 1183-1234

  Majda, Andrew J ^a   Holen, Margaret ^b  

^a NEW YORK UNIVERSITY   (United States)

^b PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031507314     PISSN: 00103640     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0312(199712)50:12<1183::AID-CPA1>3.0.CO;2-4     Document Type: Article

References (36)

1. Abramowitz, M., and Stegun, I. A., eds., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (reprint of the 1972 edition), Dover, New York, 1992.
2. Arnold, V. I., Mathematical Methods of Classical Mechanics, 2nd ed., Graduate Texts in Mathematics No. 60, Springer, New York-Berlin, 1989.
3. Bretherton, F. P., and Haidvogel, D. B., Two-dimensional turbulence above topography, J. Fluid Mech. 78, 1976, pp. 129-154.
4. Caglioti, E., Lions, P. L., Marchioro, C., and Pulvirenti, M., A special class of stationary flows for two-dimensional Euler equations: A statistical mechanics description, Comm. Math. Phys. 143, 1992, pp. 501-525.
5. Caglioti, E., Lions, P. L., Marchioro, C., and Pulvirenti, M., A special class of stationary flows for the two-dimensional Euler equations: A statistical mechanics description, II, Comm. Math. Phys. 174, 1995, pp. 229-260.
6. Carnevale, G., and Frederiksen, J., Nonlinear stability and statistical mechanics of flow over topography, J. Fluid Mech. 175, 1987, pp. 157-181.
7. E, W., and Shu, C.-W., Effective equations and the inverse cascade theory for Kolmogorov flows, Phys. Fluids A 5, 1993, pp. 998-1010.
8. Eydeland, A., Spruck, J., and Turkington, B., Multiconstrained variational problems of nonlinear eigenvalue type: New formulations and algorithms, Math. Comp. 55, 1990, pp. 509-535.
9. Foias, C., and Saut, J. L., Asymptotic behavior as t → ∞ of solutions of Navier-Stokes equations and nonlinear spectral manifolds, Indiana Univ. Math. J. 33, 1984, pp. 459-477.
10. Griffa, A., and Salmon, R., Wind-driven ocean circulation and equilibrium statistical mechanics, J. Marine Res. 47, 1989, pp. 457-492.
11. Grote, M., and Majda, A., Crude closure dynamics through large scale statistical theories, Phys. Fluids, 1997, to appear.
12. Holen, M., Comparison of statistical theories for large scale two-dimensional flows, Doctoral Dissertation, Princeton University, 1995.
13. Holloway, G., Eddies, waves, circulation, and mixing: Statistical geofluid mechanics, pp. 91-147 in: Annual Review of Fluid Mechanics, vol. 18, Annual Reviews, Palo Alto, Calif., 1986.
14. Holloway, G., Overview of statistical mechanics with practical application for ocean modeling, preprint, 1994.
15. Jaynes, E. T., Detection of extra-solar system planets, pp. 147-160 in: Maximum-Entropy and Bayesian Methods in Science and Engineering, vol. 1 (Laramie, WY, 1985, and Seattle, WA, 1986/1987), G. J. Erickson and C. R. Smith, eds., Fundamental Theories of Physics, Kluwer, Dordrecht, 1988.
16. Jaynes, E. T., Detection of extra-solar system planets, pp. 147-160 in: Maximum-Entropy and Bayesian Methods in Science and Engineering, vol. 1 (Laramie, WY, 1985, and Seattle, WA, 1986/1987), G. J. Erickson and C. R. Smith, eds., Fundamental Theories of Physics, Kluwer, Dordrecht, 1988.
17. Kraichnan, R. H., Statistical dynamics of two-dimensional flow, J. Fluid Mech. 67, 1975, pp. 155-175.
18. Kraichnan, R. H., and Montgomery, D., Two-dimensional turbulence, Rep. Prog. Phys. 43, 1980, pp. 547-619.
19. Leith, C. E., Minimum enstrophy vortices, Phys. Fluids 27, 1984, pp. 1388-1395.
20. Majda, A., and Embid, P., Lectures on P.D.E.'s in Atmosphere/Ocean Science, to appear.
21. Matthaeus, W. H., Stribling, W. T., Martinez, D., Oughton, S., and Montgomery, D., Decaying two-dimensional Navier-Stokes turbulence at very long times, Phys. D 51, 1991, pp. 531-538.
22. Miller, J., Statistical mechanics of Euler equations in two dimensions, Phys. Rev. Lett. 65, 1990, pp. 2137-2140.
23. Miller, J., Weichman, P. B., and Cross, M. C., Statistical mechanics, Euler's equation, and Jupiter's Red Spot, Phys. Rev. A 45, 1992, pp. 2328-2359.
24. Montgomery, D., and Joyce, G., Statistical mechanics of "negative temperature" states, Phys. Fluids 17, 1974, pp. 1139-1145.
25. Onsager, L., Statistical hydrodynamics, Nuovo Cimento (9) 6, 1949, pp. 279-287.
26. Pedlosky, J., Geophysical Fluid Dynamics, 2nd ed., Springer, New York, 1987.
27. Pointin, Y. B., and Lundgren, T. S., Statistical mechanics of two dimensional vortices in a bounded container, Phys. Fluids 10, 1976, pp. 1459-1470.
28. Robert, R., A maximum-entropy principle for two-dimensional perfect fluid dynamics, J. Statist. Phys. 65, 1991, pp. 531-553.
29. Robert, R., and Sommeria, J., Statistical equilibrium states for two-dimensional flows, J. Fluid Mech. 229, 1991, pp. 291-310.
30. Rudin, W. K., Real and Complex Analysis, 3rd ed., McGraw-Hill, New York, 1987.
31. Salmon, R., Holloway, G., and Henderschott, M. C., The equilibrium statistical mechanics of simple quasi-geostrophic models, J. Fluid Mech. 75, 1976, pp. 691-703.
32. Spruck, J., The equilibrium statistical mechanics of simple quasi-geostrophic models, J. Fluid Mech. 75, 1976, pp. 691-703.
33. Spruck, J., The elliptic sinh Gordon equation and the construction of toroidal soap bubbles, pp. 275-301 in: Calculus of Variations and Partial Differential Equations (Trento, 1986), Lecture Notes in Mathematics No. 1340, Springer, Berlin-New York, 1988.
34. Ting, A. C., Chen, H. H., and Lee, Y. C., Exact solutions of a nonlinear boundary value problem: The vortices of the two-dimensional sinh-Poisson equation, Phys. D 26, 1987, pp. 37-66.
35. Treguier, A. M., Topographically generated steady currents in barotropic turbulence, Geophys. Astrophys. Fluid Dynamics 47, 1989, pp. 43-68.
36. Whitaker, N., and Turkington, B., Maximum entropy states for rotating vortex patches, Phys. Fluids 6, 1994, pp. 3963-3973.