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Comptes Rendus Physique
Volume 7, n° 3-4
pages 422-432 (avril-mai 2006)
Doi : 10.1016/j.crhy.2006.01.007
Statistical mechanics of the shallow-water system with an a priori potential vorticity distribution
Mécanique statistique dʼun système à eau peu profonde avec une distribution de vorticité potentielle fixée à priori

Pierre-Henri Chavanis a , Bérengère Dubrulle b,
a Laboratoire de physique théorique (UMR 5152), université Paul-Sabatier, 118, route de Narbonne, 31062 Toulouse, France 
b DRECAM/SPEC/CEA Saclay, and CNRS (URA2464), 91190 Gif sur Yvette cedex, France 

Corresponding author.

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 (PV) 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. To cite this article: P.-H. Chavanis, B. Dubrulle, C. R. Physique 7 (2006).

The full text of this article is available in PDF format.

Nous adaptons la mécanique statistique dʼun système à eau peu profonde au cas où le flot est forcé à petite échelle. Nous supposons que la statistique du forçage est représentée par une distribution de vorticité potentielle fixée à priori, qui remplace la spécification des contraintes de Casimir dans le cas des flots libres. Ceci détermine une fonctionnelle dʼentropie généralisée qui est maximisée par le champ de vorticité potentielle lissé à lʼéquilibre statistique. Nous dérivons les équations de relaxation vers lʼéquilibre qui conservant les contraintes robustes (énergie, masse et circulation) et accroissant lʼentropie généralisée. Pour citer cet article : P.-H. Chavanis, B. Dubrulle, C. R. Physique 7 (2006).

The full text of this article is available in PDF format.

Keywords : 2D turbulence, Geophysical flows, Statistical mechanics

Mots-clés : Turbulence en 2D, Écoulement géophysiques, Mécanique statistique

© 2006  Académie des sciences@@#104156@@
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