Vertically and Horizontally Inhomogeneous Heating

Abstract

In the nature and in many technical applications there are quite often situations when there is an external heating not only in the horizontal but also in the vertical. From the theoretical point of view, this problem is equivalent to the one named after Eady, however the assumption of the constant vertical temperature gradient within the fluid does not agree well with the experimental results. Therefore, for comparison of these results with the theory one considers not only the external temperature gradient ${{\partial {T_0}} \over {\partial z}}$ but also the local internal one ${{\partial T} \over {\partial z}}$ formed in the experiments by convective motions and determined by the horizontal gradient ${{\partial {T_0}} \over {\partial r}}$. Therefore, it is natural to continue considering convective motions in rotating fluids with a mixed heating. The simplest variant of heating will be that when the external temperature will be constant at the edge of the heated surfaces. Two limiting cases are possible here: first, modification of the problem of a plane rotating layer with inhomogeneously heated bottom when a jet stream arises near the heated horizontal surface, and, second, an inhomogeneously heated annulus with constant temperature gradient at the side walls. In the first case, the temperature vertical gradient inside the fluid changes strongly in the radial direction. In the second case, the radial change is not large, but the external temperature vertical gradient (which can be of both signs) influences strongly the motion patterns.