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 continues and generalizes the study "On the Similarity of Quasi-Geostrophic Vortices against the Background of Large-Scale Barotropic Currents" [6] (Oceanology, Zhmur, 2024, in print). In continuation of [6], 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 arbitrarily 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 barotropic and baroclinic components-is presented. Ultimately, the problem boils down to an integrodifferential equation for the evolution of the vortex core boundary. The study of this equation in dimensionless form makes it possible to find a set of dimensionless parameters that determine the similarity condition of the studied vortices.