Geodesic
Phase Transition to Quadrupolar Vortices in a Spherical Model of the Energy-Enstrophy Theory — Exact Solution
Russian journal of nonlinear dynamics, Tome 16 (2020) no. 4, pp. 543-555

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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, rotating atmospheres.
Mots-clés : phase transition 
@article{ND_2020_16_4_a1,
     author = {C. C. Lim},
     title = {Phase {Transition} to {Quadrupolar} {Vortices} in a {Spherical} {Model} of the {Energy-Enstrophy} {Theory} {\textemdash} {Exact} {Solution}},
     journal = {Russian journal of nonlinear dynamics},
     pages = {543--555},
     publisher = {mathdoc},
     volume = {16},
     number = {4},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2020_16_4_a1/}
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C. C. Lim. Phase Transition to Quadrupolar Vortices in a Spherical Model of the Energy-Enstrophy Theory — Exact Solution. Russian journal of nonlinear dynamics, Tome 16 (2020) no. 4, pp. 543-555. http://geodesic.mathdoc.fr/item/ND_2020_16_4_a1/