Statistical Equilibrium of trapped slender vortex filaments - a continuum model
Loading...
Date
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
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.
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
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