海盆中Fofonoff流的统计力学
Statistical mechanics of Fofonoff flows in an oceanic basin
摘要：
本文研究了具有任意地形的海盆中在固定环流和能量条件下位涡拟能的最小化问题。为了说明，我们考虑一个矩形盆地和一个线性地形h=由它代表一个真正的底部地形或β效应适合于海洋的情况。我们的最小涡度拟能原理是由本文所回顾的统计力学的不同论点所激发的。它导致准地转（QG）方程的定常状态，其特征在于位涡q和流函数psi之间的线性关系。对于较低的能量值，我们恢复了显示出强烈的西向急流的Fofonoff流[J.Mar.Res.13，254（1954）]。对于大的能量值，我们获得了类似于Chavanis和Sommeria [J.Fluid Mech.314，267（1996）]在没有形貌的情况下发现的单极子和偶极子之间的几何诱导的相变。在地形的存在下，我们恢复和确认Venaille和Bouchet [物理评论快报。102，104501（2009）]使用不同的形式。此外，我们引入了最小位涡拟能的松弛方程，并进行了数值模拟，以说明相变在一个矩形的海洋盆地与线性地形（或β效应）。
英文摘要：
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 beta-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 psi. 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 beta-effect).
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