Self-organization of the large-scale planetary and plasma drift vortices.
This paper is a semi-review. A new understanding of the self-organization mechanism of solitary (i.e., long-lived and, in this sense, soliton-like) large-scale vortices in geophysical fluid dynamics, as well as that of drift vortices in the magnetized plasma is discussed. This understanding differs from that described in a review paper by Nezlin [Chaos 4, 187-202 (1994)]. Earlier it was believed that formation of the solitary Rossby (and plasma drift) vortices was a result of equilibrium between wave dispersion and KdV-type nonlinearity. Under the influence of experimental data obtained by our team [M. V. Nezlin and E. N. Snezhkin, Rossby Vortices, Spiral Structures, Solitons (Springer-Verlag, Heidelberg, 1993)], it became obvious that the self-organization of the structures inevitably includes an essential effect of other nonlinearities; first, that presented by the Jacobian in the equations. (We replace the term "Rossby soliton" by the more exact one "the Rossby solitary vortex.") It must be noted from the very beginning that the term "self-organization" is used mainly in context with an explanation which factors (dispersion and nonlinearities of different kind) condition formation of the solitary (stable, long-lived) Rossby structures. Although, the experimental fact (see below) that the size of solitary vortices turns out to be close to the Rossby-Obukhov radius, independently of the size of the vortex local source, calls to mind the formation of an attractor. In essence, the Rossby solitary vortex self-organization process (although, only for the case of anticyclones) was described by Nycander and Sutyrin [Dyn. Atmos. Oceans 16, 473-498 (1992)]. Unfortunately, however, the authors did not use the term "self-organization." Our description, being in accord with Nycander and Sutyrin, relates not only to anticyclones, but also to anticyclones and cyclones. Second, a description of the experimental discovery of "anomalous" cyclonic-anticyclonic asymmetry is given. Unlike "normal" asymmetry which manifests, in particular, in that the big vortices dominating in giant planet atmospheres (e.g., the Great Red Spot of Jupiter, the Brown Spot of Saturn, the Great Dark Spot of Neptune, et al.) are anticyclones, the asymmetry described manifests in that large-scale solitary vortices may be as cyclones only, not anticyclones. This phenomenon is observed in the presence of a rather strong and properly directed gradient in rotating shallow water depth. This type of asymmetry exists with drift vortices in magnetized plasma. Third, the physical difference between the planetary atmosphere and the laboratory model based on the shallow water layer in a rotating paraboloid is discussed (following, in principle, the Nycander-93 work). It is shown that laboratory modeling is adequate. Fourth, it is also shown that the most essential behavior of the vortices studied on the so-called "beta-plane" of planets and in plasmas can be described by means of rather simplified and visual equations. These are the so-called generalized Charney-Obukhov equation in fluid dynamics and its plasma counterpart, the generalized Hasegawa-Mima equation. Finally, nonlinearities are revealed, which condition properties of the geostrophic vortices under study on the "f-plane," i.e., in the polar regions of planets. &c