The Similarity of Quasi-geostrophic Vortices against the Background of Horizontal Currents with Vertical Shear and General-type Currents with Barotropic and Baroclinic Components

This article is a continuation and generalization of the work “On the similarity of quasi-geostrophic vortices against the background of large-scale barotropic currents” [6] (Oceanology, Zhmur, 2024, in print). In continuation of the above work, a similar formulation is considered, but for other types of background currents. In the quasi-geostrophic description for small Rossby numbers, the problem of the evolution of an arbitrary–shaped liquid volume with homogeneous potential vorticity of all vortex core particles in an equidistant background flow – horizontal flow with vertical shear and equidistant flow with barotrotropic and baroclinic components is presented. Ultimately, the problem boils down to an integro-differential equation for the evolution of the vortex core boundary. The study of this equation in dimensionless form allows us to find a set of dimensionless parameters that determine the similarity condition of the vortices under study.