Relaxation equations for two-dimensional turbulent flows with a prior vorticity distribution

P. H. Chavanis (), A. Naso and B. Dubrulle

The European Physical Journal B: Condensed Matter and Complex Systems, 2010, vol. 77, issue 2, 167-186

Abstract: Using a Maximum Entropy Production Principle (MEPP), we derive a new type of relaxation equations for two-dimensional turbulent flows in the case where a prior vorticity distribution is prescribed instead of the Casimir constraints [R. Ellis, K. Haven, B. Turkington, Nonlinearity 15, 239 (2002)]. The particular case of a Gaussian prior is specifically treated in connection to minimum enstrophy states and Fofonoff flows. These relaxation equations are compared with other relaxation equations proposed by Robert and Sommeria [Phys. Rev. Lett. 69, 2776 (1992)] and Chavanis [Physica D 237, 1998 (2008)]. They can serve as numerical algorithms to compute maximum entropy states and minimum enstrophy states with appropriate constraints. We perform numerical simulations of these relaxation equations in order to illustrate geometry induced phase transitions in geophysical flows. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2010

Date: 2010
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DOI: 10.1140/epjb/e2010-00264-5

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