Abstract
Abstract
In a liquid (gaseous) medium above a thermally inhomogeneous horizontal surface in a gravity field, convective flows arise, which can play an important role, in particular, in the dynamics of the atmosphere. An extensive literature is devoted to their theory, but, due to the complexity of the problem and the variety of possible combinations of parameters, not all situations of interest have been sufficiently studied even in the linear approximation. In this work, a theoretical model of such thermal circulations is considered, which is more general than in a number of previous works. An analytical solution is found within the framework of a linear stationary two-dimensional model of convective flows in a semi-infinite stably stratified medium rotating around a vertical axis. The obtained relations allow analyzing the dependences of the components of velocity and helicity on the parameters of the problem. A number of rather general statements about the ratio of different helicity “components” in the considered thermal circulations, in particular, in atmospheric currents with characteristic horizontal scales of the order of hundreds of kilometres, have been proved. Examples of numerical calculations of the vertical distribution of these components are given.