Statistical mechanics of the shallow-water system with a prior potential vorticity distribution
Fluid Dynamics
2009-11-13 v1
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.
Keywords
Cite
@article{arxiv.physics/0611165,
title = {Statistical mechanics of the shallow-water system with a prior potential vorticity distribution},
author = {P. H. Chavanis and B. Dubrulle},
journal= {arXiv preprint arXiv:physics/0611165},
year = {2009}
}