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The equilibrium statistical mechanics of simple quasi-geostrophic models

  • Rick Salmon (a1), Greg Holloway (a1) and Myrl C. Hendershott (a1)

Abstract

We have applied the methods of classical statistical mechanics to derive the inviscid equilibrium states for one- and two-layer nonlinear quasi-geostrophic flows, with and without bottom topography and variable rotation rate. In the one-layer case without topography we recover the equilibrium energy spectrum given by Kraichnan (1967). In the two-layer case, we find that the internal radius of deformation constitutes an important dividing scale: at scales of motion larger than the radius of deformation the equilibrium flow is nearly barotropic, while at smaller scales the stream functions in the two layers are statistically uncorrelated. The equilibrium lower-layer flow is positively correlated with bottom topography (anticyclonic flow over seamounts) and the correlation extends to the upper layer at scales larger than the radius of deformation. We suggest that some of the statistical trends observed in non-equilibrium flows may be looked on as manifestations of the tendency for turbulent interactions to maximize the entropy of the system.

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References

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Basdevant, C. & Sadourny, R. 1975 J. Fluid Mech. 69, 673.
Bretherton, F. P. & Haidvogel, D. 1976 Two-dimensional turbulence above topography. (In the press.)
Charney, J. G. 1971 J. Atmos. Sci. 28, 1087.
Fofonoff, N. P. 1954 J. Mar. Res. 13, 254.
Fox, D. G. & Orszag, S. A. 1973 Phys. Fluids, 16, 169.
Holloway, G. & Hendershott, M. C. 1974 MODE Hot Line News, no. 65.
Holloway, G. & Hendershott, M. C. 1975 A stochastic model for barotropic eddy interactions on the beta-plane. (In the press.)
Khinchin, A. I. 1949 Mathematical Foundations of Statistical Mechanics. Dover.
Kraichnan, R. H. 1967 Phys. Fluids, 10, 1417.
Kraichnan, R. H. 1975 J. Fluid Mech. 67, 155.
Orszag, S. A. 1970 J. Fluid Mech. 41, 363.
Pedlosky, J. 1970 J. Atmos. Sci. 27, 15.
Phillips, N. A. 1956 Quart. J. Roy. Met. Soc. 82, 123.
Rhines, P. B. 1975a J. Fluid Mech. 69, 417.
Rhines, P. B. 1975b The dynamics of unsteady currents. In The Sea, vol. VI (in the press).
Salmon, R. 1975 Ph.D. dissertation, University of California, San Diego.
Thompson, P. D. 1972 J. Fluid Mech. 55, 711.
Thompson, P. D. 1974 J. Atmos. Sci. 30, 1593.
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The equilibrium statistical mechanics of simple quasi-geostrophic models

  • Rick Salmon (a1), Greg Holloway (a1) and Myrl C. Hendershott (a1)

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