Description of the perturbations of oceanic geostrophic currents with linear vertical velocity shear taking into account friction and diffusion of density
A spectral problem of Orr-Sommerfeld type for describing stable and unstable disturbances of oceanic geostrophic flows with linear vertical velocity shear is considered. Calculations of eigenvalues, increments of growth rate of unstable modes, and eigenfunctions of the fastest growing disturbances are presented. It is found that the instability of the flow is observed over a wide range of horizontal scales: in addition to long-wave perturbations with a phase velocity exceeding the maximum flow velocity and perturbations with scales of the Rossby radius, short-wave modes with scales much smaller than the Rossby radius (sub-mesoscale structures) exist. The results of the model are used to describe intrusions in the Arctic basin, which are observed under conditions of absolutely stable stratification.