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The European Physical Journal B

, Volume 80, Issue 4, pp 493–517 | Cite as

Statistical mechanics of Fofonoff flows in an oceanic basin

Article

Abstract.

We study the minimization of potential enstrophy at fixed circulation and energy in an oceanic basin with arbitrary topography. For illustration, we consider a rectangular basin and a linear topography h = by which represents either a real bottom topography or the β-effect appropriate to oceanic situations. Our minimum enstrophy principle is motivated by different arguments of statistical mechanics reviewed in the article. It leads to steady states of the quasigeostrophic (QG) equations characterized by a linear relationship between potential vorticity q and stream function ψ. For low values of the energy, we recover Fofonoff flows [J. Mar. Res. 13, 254 (1954)] that display a strong westward jet. For large values of the energy, we obtain geometry induced phase transitions between monopoles and dipoles similar to those found by Chavanis and Sommeria [J. Fluid Mech. 314, 267 (1996)] in the absence of topography. In the presence of topography, we recover and confirm the results obtained by Venaille and Bouchet [Phys. Rev. Lett. 102, 104501 (2009)] using a different formalism. In addition, we introduce relaxation equations towards minimum potential enstrophy states and perform numerical simulations to illustrate the phase transitions in a rectangular oceanic basin with linear topography (or β-effect).

Keywords

Order Phase Transition Potential Vorticity Rectangular Domain Microcanonical Ensemble Relaxation Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Laboratoire de Physique, École Normale Supérieure de Lyon and CNRS (UMR 5672)LyonFrance
  2. 2.LMFA, Université de Lyon, École Centrale de Lyon, and CNRS (UMR 5509)Ecully CedexFrance
  3. 3.Laboratoire de Physique Théorique (IRSAMC), CNRS and UPS, Université de ToulouseToulouseFrance
  4. 4.SPEC/IRAMIS/CEA Saclay, and CNRS (URA 2464)Gif-sur-Yvette CedexFrance

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