Statistical mechanics of the shallow-water system with a prior potential vorticity distribution

P. H. Chavanis; B. Dubrulle

doi:10.1016/j.crhy.2006.01.007

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Statistical mechanics of the shallow-water system with a prior potential vorticity distribution

P. H. Chavanis·B. Dubrulle

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Abstract

We adapt the statistical mechanics of the shallow-water equations to the case where the flow is forced at small scales. We assume that the statistics of forcing is encoded in a prior potential vorticity distribution which replaces the specification of the Casimir constraints in the case of freely evolving flows. This determines a generalized entropy functional which is maximized by the coarse-grained PV field at statistical equilibrium. Relaxation equations towards equilibrium are derived which conserve the robust constraints (energy, mass and circulation) and increase the generalized entropy.

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P. H. Chavanis, B. Dubrulle. 2006-11-16. Statistical mechanics of the shallow-water system with a prior potential vorticity distribution. https://doi.org/10.1016/j.crhy.2006.01.007

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