Metriplectic simulated annealing for quasigeostrophic flow

Metriplectic dynamics [1,2] is a general form for dynamical systems that embodies the first and second laws of thermodynamics, energy conservation and entropy production. The formalism provides an $H$-theorem for relaxation to nontrivial equilibrium states. Upon choosing enstrophy as entropy and potential vorticity of the form $q= \nabla^2\psi +T(x)$, recent results of computations, akin to those of [3], will be described for various topography functions $T(x)$, including ridge ($T=\exp(-x^2/2)$) and random functions. Interpretation of the results, in particular their sensitivity to the chosen entropy function will be discussed. \\ \noindent [1] P.J.~Morrison, Physica D {\bf18}, 410 (1986).\\ \noindent [2] A.M.~Bloch, P.J.~Morrison, and T.S. Ratiu, in Recent Trends\\ in Dynamical Systems {\bf35}, 371 (2013).\\ \noindent [3] G.R. Flierl and P.J, Morrison, Physica D {\bf240}, 212 (2011).