Statistical Equilibrium of trapped slender vortex filaments - a continuum model

Timothy D. Andersen; Chjan C. Lim

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arXiv · cond-mat/0601109

Statistical Equilibrium of trapped slender vortex filaments - a continuum model

Timothy D. Andersen·Chjan C. Lim

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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.

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Timothy D. Andersen, Chjan C. Lim. 2006-09-25. Statistical Equilibrium of trapped slender vortex filaments - a continuum model. https://arxiv.org/abs/cond-mat/0601109

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