Toward the theory of convection in a rotating stratified medium over a thermally inhomogeneous horizontal surface

Abstract

Stationary convection in a rotating medium uniformly heated from above and nonuniformly cooled from below has been studied analytically in the linear approximation. As distinct from a number of previous works, the case of the presence of both a stable background stratification and of intense rotation around a vertical axis has been analyzed. One of the interesting properties of the solution found is that despite the stable stratification the perturbations of temperature, pressure, and of the vertical velocity over the thermal inhomogeneities of the horizontal surface, in the case of strong rotation, penetrate deep into the medium (up to heights of the order of the horizontal scales of the inhomogeneities mentioned.) The ascending motions over the "warm spot" transfer relatively cold volumes of the medium upwards, so that beginning from a certain level a vast "cold" region can be formed and the related positive deviation of pressure (of the weight of the medium column). This leads to the formation of the anticyclonic vortex perturbation.