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Statistical mechanics of twodimensional and geophysical flows
, 2005
"... The theoretical study of the selforganization of twodimensional and geophysical turbulent flows is addressed based on statistical mechanics methods. This review is a selfcontained presentation of classical and recent works on this subject; from the statistical mechanics basis of the theory up to ..."
Abstract

Cited by 36 (17 self)
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The theoretical study of the selforganization of twodimensional and geophysical turbulent flows is addressed based on statistical mechanics methods. This review is a selfcontained presentation of classical and recent works on this subject; from the statistical mechanics basis of the theory up to applications to Jupiterâ€™s troposphere and ocean vortices and jets. Emphasize has been placed on examples with available analytical treatment in order to favor better understanding of the physics and dynamics. After a brief presentation of the 2D Euler and quasigeostrophic equations, the specificity of twodimensional and geophysical turbulence is emphasized. The equilibrium microcanonical measure is built from the Liouville theorem. Important statistical mechanics concepts (large deviations, mean field approach) and thermodynamic concepts (ensemble inequivalence, negative heat capacity) are briefly explained and described. On this theoretical basis, we predict the output of the long time evolution of complex turbulent flows as statistical equilibria. This is applied to make quantitative models of twodimensional turbulence, the Great Red Spot and other Jovian vortices, ocean jets like the Gulf
Curvature and Statistics
, 2013
"... This thesis consists of two parts: In part I we apply the statistical mechanics techniques to a generalization of the prescribed Qcurvature problem, especially on the ddim sphere Sd. We introduce a coupling constant c on top of the configurational canonical ensemble and study the weak convergence ..."
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This thesis consists of two parts: In part I we apply the statistical mechanics techniques to a generalization of the prescribed Qcurvature problem, especially on the ddim sphere Sd. We introduce a coupling constant c on top of the configurational canonical ensemble and study the weak convergence of this new canonical ensemble. In this part, the Qcurvature does not change sign. In part II the statistical mechanics technique is generalized to the prescribed Qcurvature problem with signchange, while the mechanical interpretation will be lost. We decompose a single differential equation into a system of two differential equations, and the statistical mechanics technique can be applied to each equation.