 
Summary: Physica D xxx (2004) xxxxxx
Nonextensive statistical mechanics for rotating
quasitwodimensional turbulence
Sunghwan Jung, Brian D. Storey, Julien Aubert, Harry L. Swinney
Department of Physics, Center for Nonlinear Dynamics, The University of Texas at Austin, Austin, TX 78712, USA
Communicated by C.K.R.T. Jones
Abstract
We have conducted experiments on an asymmetrically forced quasitwodimensional turbulent flow in a rapidly rotat
ing 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 ac
cord with the observations. A nonextensive formalism is appropriate because longrange correlations between smallscale
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.
© 2004 Published by Elsevier B.V.
Keywords: Turbulence; Rotating flows; Tsallis entropy; Nonextensive
1. Introduction
Equilibrium statistical mechanics has long been used to describe turbulence [1]. Early work by Onsager pre
dicted coherent structure formation through consideration of the interactions of point vortices [2]. Later Kraichnan
