Statistical equilibrium distributions of baroclinic vortices in a rotating two-layer model at low Froude numbers

The point-vortex equilibrium statistical model of two-layer baroclinic quasigeostrophic vortices in an unbounded f-plane is examined. A key conserved quantity, angular momentum, serves to confine the vortices to a compact domain, thereby justifying the statistical mechanics model, and also eliminating the need for boundary conditions in a practical method for its resolution. The Metropolis method provides a fast and efficient algorithm for solving the mean field non-linear elliptic PDEs of the equilibrium statistical theory. A verification of the method is done by comparison with the exact Gaussian solution at the no interaction limit of zero inverse temperature. The numerical results include a geophysically and computationally relevant power law for the radii at which the most probable vortex distribution is non-vanishing: For fixed total circulation, and fixed average angular momentum, the radii of both layers are proportional to the square root of the inverse temperature β. By changing the chemical potentials μ of the runs, one is able to model the most probable vorticity distributions for a wide range of total circulation and energy. The most probable vorticity distribution obtained at low positive temperatures are consistently close to a radially symmetric flat-top profiles. At high temperatures, the radially symmetric vorticity profiles are close to the Gaussian distribution.