Vortex tori above bottom perturbations in a rotating fluid

Abstract

In this study, a model that describes one of the mechanisms of diapycnal mixing in topographic vortices above seamounts in the Ocean is presented. It is known that topographic eddies are described in the quasi-geostrophic approximation; i.e., vertical velocities are considered to be negligibly small (of about the Rossby number). However, the data of observations indicate the presence of a well-mixed fluid column in the vicinity of seamounts. Description of such vertical mixing is possible only due to account of the vertical velocity component. The spectral problem for the stability of a topographic vortex over the perturbation of the bottom relief in the form of a simple cylinder and for a more complex configuration consisting of two coaxial cylinders is solved. It is shown that the eigenvalues of the spectrum are the bifurcation points of the flow, due to which secondary toroidal vortices are generated. These toroidal vortices perform intense vertical mixing of waters above seamounts in the Ocean. The method of invariant imbedding is used to solve the spectral problem.