dorsal/arxiv
View SchemaStatistical mechanics of the shallow-water system with a prior potential vorticity distribution
| Authors | P. H. Chavanis, B. Dubrulle |
|---|---|
| Categories | |
| ArXiv ID | physics/0611165 |
| URL | https://arxiv.org/abs/physics/0611165 |
| DOI | 10.1016/j.crhy.2006.01.007 |
| Journal | C. R. Physique, 7, 422 (2006) |
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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"abstract": "We adapt the statistical mechanics of the shallow-water equations to the case\nwhere the flow is forced at small scales. We assume that the statistics of\nforcing is encoded in a prior potential vorticity distribution which replaces\nthe specification of the Casimir constraints in the case of freely evolving\nflows. This determines a generalized entropy functional which is maximized by\nthe coarse-grained PV field at statistical equilibrium. Relaxation equations\ntowards equilibrium are derived which conserve the robust constraints (energy,\nmass and circulation) and increase the generalized entropy.",
"arxiv_id": "physics/0611165",
"authors": [
"P. H. Chavanis",
"B. Dubrulle"
],
"categories": [
"physics.flu-dyn"
],
"doi": "10.1016/j.crhy.2006.01.007",
"journal_ref": "C. R. Physique, 7, 422 (2006)",
"title": "Statistical mechanics of the shallow-water system with a prior potential vorticity distribution",
"url": "https://arxiv.org/abs/physics/0611165"
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