2006/01/06 by Timothy D. Andersen, Andersen, Timothy D., Chjan C. Lim +1
Engineering · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Quantum, superfluid, helium dynamics #Statistical Mechanics (cond-mat.stat-mech) #Superconductivity (cond-mat.supr-con)
paper · pdf · doi:10.48550/arxiv.cond-mat/0601109
openalex publication_date 2006/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.