The paper proposes a theory of similarity of quasi-geostrophic vortices against the background of large-scale flows. This information is useful when planning laboratory and numerical experiments to study mesoscale and submesoscale vortex dynamics of vortices interacting with currents. Special attention is paid to the study of geometric similarity of phenomena. It is revealed that the complete set of dimensionless similarity numbers of baroclinic vortices includes four dimensionless parameters: the dimensionless intensity of the vortex, the geometric similarity of the background flow (the ratio of relative vorticity to the deformation coefficient of the background flow), the coefficient of horizontal elongation of the vortex core and the coefficient of vertical oblateness of the vortex core coinciding with the Burger number. To describe the similarity of barotropic vortices against the background of barotropic flows, the number of necessary dimensionless parameters is reduced by one number — the coefficient of vertical oblateness of the vortex core is eliminated from consideration. When studying axisymmetric vortices or vortex structures close to axisymmetric, another geometric parameter of the vortex is eliminated from consideration — the coefficient of horizontal elongation of the vortex core. As a result, the maximum possible set of similarity parameters includes four dimensionless numbers, and the minimum is two.
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