Nonextensive statistical mechanics for rotating quasi-two-dimensional turbulence

Abstract

We have conducted experiments on an asymmetrically forced quasi-two-dimensional turbulent flow in a rapidly rotating annulus. Assuming conservation of potential enstrophy and energy, we maximize a nonextensive entropy function to obtain the azimuthally averaged vorticity as a function of radial position. The predicted vorticity profile is in good accord with the observations. A nonextensive formalism is appropriate because long-range correlations between small-scale vortices give rise to large coherent structures in the turbulence. We also derive probability distribution functions for the vorticity from both extensive and nonextensive entropies, and we find that the prediction from nonextensive theory is in better accord with experiment, especially in the tails of the distribution function. The nonextensive parameter q has the value 1.9±0.2.