Kuzmina N. P.
Some analytical solutions are found for the problem of three-dimensional instability of a weak geostrophic flow with linear velocity shear taking into account the vertical diffusion of buoyancy. The analysis is based on the potential vorticity equation in a long-wave approximation when the horizontal scale of disturbances is taken much larger than the local baroclinic Rossby radius. It is hypothesized that the solutions found can be applied to describe stable and unstable disturbances of planetary scale with respect, especially, to the Arctic Basin where weak baroclinic fronts with typical temporal variability period of the order of several years or more are observed and the beta-effect is negligible. The unstable (growing with time) solutions are applied to describe the large-scale intrusions typical for the Arctic Basin. Double diffusion being typical and important driver of oceanic intrusions is included to the model by means of a simplest parameterization. Solutions obtained with and without effect of double diffusion are compared with structural features of large-scale intrusive layers observed in the Arctic Basin. Stable (decaying with time) solutions describe disturbances that, in contrast to the Rossby waves, can propagate both to the west and east depending on the sign of linear shear of geostrophic velocity. It is supposed that the analytical solutions found can be useful to validate numerical solutions of the eigen value problems devoted to the analysis of three-dimensional instability of slow baroclinic fronts with the consideration of vertical diffusion of buoyancy. Moreover, the analytical solutions obtained give analytical formulas for the phase velocities and growth/decay rates of disturbances that cannot, as a rule, be found exactly from numerical solutions of the eigen value problems.