Maximum entropy versus minimum enstrophy vortices

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 princ iple provides a good and useful approximation of the statistical theory, ex cept for large energies. In the case investigated by Huang and Driscoll, th is approximation even yields a better agreement with experiments than the f ull statistical theory because the relaxation of the system toward the maxi mum entropy state is not complete. However, we show that this agreement can not hold in more general cases, due to physical inconsistencies of minimum enstrophy principles. We also discuss the relevance of generalized thermody namics (Tsallis entropy) to predict the equilibrium state. (C) 1999 America n Institute of Physics. [S1070-6631(99)01710-9].