Relaxation towards localized vorticity states in drift plasma and geostrophic flows.

The drift of ions in a magnetized plasma or the height fluctuations of a rotating fluid layer are described by the conservation equation of a potential vorticity. This potential vorticity contains an intrinsic length scale, the hybrid Larmor radius in plasma, and the Rossby length in the quasigeostrophic flow. The influence of this scale in the evolution of a random initial vorticity field is investigated using a thermodynamic approach. In contrast to the perfect fluid case, where the vorticity tends to a well defined stationary state, complete relaxation towards an equilibrium state is not observed in numerical simulations of quasigeostrophic decaying turbulence. The absence of global thermodynamic equilibrium is explained by the relaxation towards states of local equilibrium where the vorticity is concentrated. The interaction between these separated regions is extremely weak. Explicit, axisymmetric, localized solutions of the mean field integrodifferential equation of extremal entropy states are obtained using asymptotic methods. A comparison of the computed solutions with the observed coherent structures shows that they effectively correspond to states in local thermodynamic equilibrium.