Statistical Equilibrium of trapped slender vortex filaments - a continuum model
Abstract
Systems of nearly parallel, slender vortex filaments in which angular momentum is conserved are an important simplification of the Navier-Stokes equations where turbulence can be studied in statistical equilibrium. We study the canonical Gibbs distribution based on the Klein-Majda-Damodaran (KMD) model and find a divergence in the mean square vortex position from that of the point vortex model of Onsager at high temperature. We subsequently develop a free energy equation based on the non-interacting case, with a spherical constraint, which we approximate using the method of Kac-Berlin, adding a mean field term for logarithmic interaction. This free energy equation, we use to predict the Monte Carlo results.
Cite
@article{arxiv.cond-mat/0601109,
title = {Statistical Equilibrium of trapped slender vortex filaments - a continuum model},
author = {Timothy D. Andersen and Chjan C. Lim},
journal= {arXiv preprint arXiv:cond-mat/0601109},
year = {2007}
}
Comments
13 pages, 5 figures; major revisions in theoretical section; slight change of numerical results from L=20 to L=100; typos corrected in free-energy section