Phase Transition to Quadrupolar Vortices in a Spherical Model of the Energy-Enstrophy Theory — Exact Solution
Received 10 October 2020; accepted 05 December 2020
2020, Vol. 16, no. 4, pp. 543-555
Author(s): Lim C. C.
A new energy-enstrophy model for the equilibrium statistical mechanics of barotropic flow
on a sphere is introduced and solved exactly for phase transitions to quadrupolar vortices when
the kinetic energy level is high. Unlike the Kraichnan theory, which is a Gaussian model, we
substitute a microcanonical enstrophy constraint for the usual canonical one, a step which is based
on sound physical principles. This yields a spherical model with zero total circulation, a microcanonical
enstrophy constraint and a canonical constraint on energy, with angular momentum fixed
to zero. A closed-form solution of this spherical model, obtained by the Kac – Berlin method
of steepest descent, provides critical temperatures and amplitudes of the symmetry-breaking
quadrupolar vortices. This model and its results differ from previous solvable models for related
phenomena in the sense that they are not based on a mean-field assumption.
Download File PDF, 312.84 Kb |
This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License