  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.
