PROBLEMS OF SIMULATION OF LARGE, LONG-LIVED VORTICES IN THE ATMOSPHERES OF THE GIANT PLANETS (JUPITER, SATURN, NEPTUNE)

Large, long-lived vortices are abundant in the atmospheres of the gian t planets. Some of them survive a few orders of magnitude longer than the dispersive linear Rossby wave packets, e,g. the Great Red Spot (GR S), Little Red Spot (LRS) and White Ovals (WO) of Jupiter, Big Bertha, Brown Spot and Anne's Spot of Saturn, the Great Dark Spot (GDS) of Ne ptune, etc. Nonlinear effects which prevent their dispersion spreading are the main subject of our consideration. Particular emphasis is pla ced on determining the dynamical processes which may explain the remar kable properties of observed vortices such as anticyclonic rotation in preference to cyclonic one and the uniqueness of the GRS, the largest coherent vortex, along the perimeter of Jupiter at corresponding lati tude. We review recent experimental and theoretical studies of steadil y translating solitary Rossby vortices (anticyclones) in a rotating sh allow fluid. Two-dimensional monopolar solitary vortices trap fluid wh ich is transported westward. These dualistic structures appear to be v ortices, on the one hand, and solitary ''waves'', on the other hand. O wing to the presence of the trapped fluid, such solitary structures co llide inelastically and have a memory of the initial disturbance which is responsible for the formation of the structure. As a consequence, they have no definite relationship between the amplitude and character istic size. Their vortical properties are connected with geostrophic a dvection of local vorticity. Their solitary properties (nonspreading a nd stationary translation) are due to a balance between Rossby wave di spersion and nonlinear effects which allow the anticyclones, with an e levation of a free surface, to propagate faster than the linear waves, without a resonance with linear waves, i.e. without wave radiation. O n the other hand, cyclones, with a depression of a free surface, are d ispersive and nonstationary features. This asymmetry in dispersion-non linear properties of cyclones and anticyclones is thought to be one of the essential reasons for the observed predominance of anticyclones a mong the long-lived vortices in the atmospheres of the giant planets a nd also among the intrathermocline oceanic eddies. The effects of shea r flows and differences between the properties of monopolar vortices i n planetary flows and various laboratory experiments are discussed. Ge neral geostrophic (GG) theory of Rossby vortices is presented. It diff ers essentially from the traditional quasi-geostrophic (QG) and interm ediate-geostrophic (IG) approximations by the account of (i) all scale s between the deformation radius and the planetary scale and (ii) the arbitrary amplitudes of vortices. It is shown that, unlike QG- and IG- models, the GG-model allows for explaining the mentioned cyclonic-anti cyclonic asymmetry not only in planetary flows, but also in laboratory modeling with vessels of near paraboloidal form.