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.
Keywords:
energy-enstrophy theory, long-range spherical model, phase transition, rotating atmospheres
Citation:
Lim C. C., Phase Transition to Quadrupolar Vortices in a Spherical Model of the Energy-Enstrophy Theory — Exact Solution, Rus. J. Nonlin. Dyn.,
2020, Vol. 16, no. 4,
pp. 543-555
DOI:10.20537/nd200402