Analogy between drift vortices in plasma and geophysical hydrodynamics

The paper contains a review and original results. A complete analogy is shown between the nonlinear equations describing drift vortices in a magnetized plasma, on the one hand, and the Rossby vortices in ''shallow water,'' on the other. Adequacy is shown of laboratory modeling of drift vortices in a plasma by means of shallow-water experiments using rotating vessels of parabolic shape. The mechanism for self-organization of the solitary (i.e., long-living, soliton-like) drift vortices in a magnetized plasma and in the geophysical fluid dynamics has been considered. According to the new understanding of this mechanism, the self-organization of the solitary structures under consideration cannot be a result only of mutual compensation of the wave dispersion and the ''scalar'' nonlineraity of the Korteveg-de Vries (KdV) type. Actually, it inevitably includes, besides the Rossby wave dispersion, an interaction (in particular, a competition) of two nonlinearities: ''scalar'' and ''vector'' ones; the first is of the KdV-type, the second is represented by the Jacobian in the equations. As a result, in the general case, a solitary structure under consideration is essentially anisotropic and is a superposition of an axially symmetrical vortex and a dipolar perturbation. A degree of the anisotropy grows essentially when the vortex size increases an approaches the so-called intermediate geostrophic radius. A misunderstanding of some preceding papers is removed, and it is shown that the solitary drift vortices in a magnetized plasma are cyclones (not anticyclones) when the gradients of the electron density and temperature have the same signs. It is shown that the solitary vortices under consideration propagate at a speed greater that the maximum speed of the corresponding linear waves. This agrees with the usual behavior of solitones.