# Equilibrium of trapped slender vortex filaments - a continuum model

#### Abstract

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-MajdaDamodaran (KMD) ([7]) model and find a divergence in the mean square vortex position from that of the point vortex model of [11] at moderate to 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 [1], adding a mean-field term for logarithmic interaction. We use this free-energy equation to predict the Monte Carlo results.

### Cite this paper

@inproceedings{Lim2006EquilibriumOT, title={Equilibrium of trapped slender vortex filaments - a continuum model}, author={C. Lim}, year={2006} }