ASYMPTOTIC EXPANSIONS AND MONOPOLAR SOLITARY ROSSBY VORTICES IN BAROTROPIC AND 2-LAYER MODELS

Motivated by observational and experimental data on large-scale Vortic es close to the geostrophic balance we perform an asymptotic analysis of the barotropic and baroclinic rotating shallow-water systems in ord er to describe slowly-evolving monopolar coherent structures. The sphe rical and the paraboloidal geometries which are, respectively, relevan t for planets and experiments with fast rotation are both studied. We analyse in detail the problem of long-living localised Vortices of axi symmetric shape and find the anticyclonic solutions of a prescribed fo rm on the sphere. In the paraboloidal geometry an arbitrary strongly n on-linear axisymmetric structure may drift preserving its form for lon g enough times. We extend this study to the baroclinic two-layer model and find similar results with an important distinction that solitary vortices may be cyclones as well, their sign depending on the physical parameters of the model. The applications of this results in astrophy sical, oceanographic and laboratory context are discussed.