Physics – Fluid Dynamics
Scientific paper
2009-12-27
Eur. Phys. J. B 77, 167-186 (2010)
Physics
Fluid Dynamics
21 pages, 9 figures
Scientific paper
10.1140/epjb/e2010-00264-5
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.
Chavanis Pierre-Henri
Dubrulle Bérangère
Naso Aurore
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