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

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 [Ellis, Haven, Turkington, Nonlin., 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 provide a small-scale parametrization of 2D turbulence or serve as numerical algorithms to compute maximum entropy states with appropriate constraints. We perform numerical simulations of these relaxation equations in order to illustrate geometry induced phase transitions in geophysical flows.

21 pages, 9 figures

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Cited by in corpus (5)

• Kinetic theory of collisionless relaxation for systems with long-range interactions
• Statistical mechanics of Fofonoff flows in an oceanic basin
• Phase transitions and marginal ensemble equivalence for freely evolving flows on a rotating sphere
• Statistical mechanics of two-dimensional point vortices: relaxation equations and strong mixing limit
• Statistical Measures and Selective Decay Principle for Generalized Euler Dynamics: Formulation and Application to the Formation of Strong Fronts