The Stability of Thermoclinic Jets

Abstract

A laminar jet, in a “shallow layer” of water of density ρ − Δρ is in geostrophic equilibrium above a much deeper and resting layer of water of density ρ. We compare the quasi-hydrostatic energy releasing process in this thermoclinic model with other baroclinic and barotropic models. It is first shown that a small amplitude disturbance can grow only if there is a transfer of kinetic energy from the horizontal variations in the mean jet and that conversions of mean potential energy can only occur concomitantly with, or as a finite amplitude result of this process. We also examine the perturbation equation for values of the stream Rossby number which are much less than unity and show that the finite depth of the thermocline inhibits inflectional instability of the jet. The generalization of Lord Rayleigh's theorem shows that the jet is stable if the gradient of potential vorticity does not vanish. In general, there is a critical value of the ratio of the radius of deformation $$\left(f^{-1}\sqrt{g{H}_0\Delta \partial /\partial }\right)$$to the half width of the jet above which quasigeostrophic disturbances will start to grow. It is proposed that meanders of the synoptic Gulf Stream will develop when the jet becomes “excessively” deep and that the effect of such instabilities is to limit the depth of the main thermocline in the interior of the ocean.