Maximum entropy versus minimum enstrophy vortices

Abstract

Motivated by the experimental study of Huang and Driscoll [Phys. Rev. Lett. 72, 2187 (1994)], we carry a systematic comparison between maximum entropy and restricted minimum enstrophy vortices. We find that, when the angular momentum constraint is reconsidered, the restricted minimum enstrophy principle provides a good and useful approximation of the statistical theory, except for large energies. In the case investigated by Huang and Driscoll, this approximation even yields a better agreement with experiments than the full statistical theory because the relaxation of the system toward the maximum entropy state is not complete. However, we show that this agreement cannot hold in more general cases, due to physical inconsistencies of minimum enstrophy principles. We also discuss the relevance of generalized thermodynamics (Tsallis entropy) to predict the equilibrium state.