ANALYTICAL MODEL OF SHEAR FLOW OVER A THERMALLY HETEROGENEOUS SURFACE

As is well known, one of the most important factors in the development of dangerous convective phenomena in the atmosphere is the vertical shear of the background wind speed. Therefore, the problems of theoretical description of the interaction of convection, thermal circulations with a shear flow are very relevant. A linear stationary problem of the interaction between a horizontal flow with a vertical shear and thermal circulations (density currents) existing over a thermally inhomogeneous horizontal surface is considered. It is assumed that in the absence of thermal inhomogeneities, there is a background flow with a constant vertical shear of velocity (Couette flow) in a stably stratified medium. Stationary disturbances caused by thermal inhomogeneities of the underlying surface, extended along the background flow, are studied. Thus, a linear stationary two-dimensional problem is considered in the Boussinesq approximation. Coriolis accelerations are not taken into account, since relatively small horizontal scales of inhomogeneities are assumed. The consideration is limited to one horizontal harmonic of disturbances. An essential dimensionless determining parameter is an analogue of the Rayleigh number R, in which the horizontal scale of the harmonic under consideration acts as a spatial scale. An approximate analytical solution is found. An essential new result is as follows: although thermal circulations penetrate relatively shallowly into a stably stratified medium, they can cause stationary disturbances of the background flow, which penetrate much deeper into the medium.

thermal circulations, shear flow, interaction, stratified medium, linear approximation, analytical model