On the Influence of Gravity Field Inhomogeneities on the Heat Exchange of the Atmosphere with an Underlying Surface

Abstract

In recent theoretical studies of the authors, some estimates of the atmospheric disturbances related to inhomogeneities of the gravity field (IGF) have been obtained. The main attention was paid to dynamic effects: disturbances of the wind field under the influence of IGF. In this paper, attention is drawn to the fact that noticeable thermal effects of IGF can also exist in the surface layer of the atmosphere. These inhomogeneities, deforming the fields of pressure, air density, and air temperature, affect the temperature regime of the boundary layer and the heat exchange of air with the underlying surface. An analytical model designed to estimate the magnitudes of these effects is considered. Based on the proposed model, an analytical solution is found for a linear stationary two-dimensional problem for perturbations caused by one horizontal harmonic of the IGF in a semi-infinite stably stratified medium rotating around a vertical axis. The temperature of the lower boundary (underlying surface) was assumed to be fixed. It was also assumed for this boundary that the no-slip and no-flow conditions are satisfied. The attenuation of all disturbances with height was also assumed. The essential similarity parameters in this problem are analogues of the Rayleigh and Taylor numbers, in which the given horizontal scale of IGF serves a spatial scale. Analytical expressions are obtained for the profiles of temperature perturbations and amplitudes of deviations of vertical heat fluxes on the surface. The latter, along with amplitudes of gravity field inhomogeneities, depend most strongly on the background stratification of the medium. In highly anomalous regions, the amplitudes of heat flux deviations, according to the estimates obtained, may reach and even exceed 1 W/m², which gives grounds for taking into account the gravity field inhomogeneities in climatic calculations and numerical models of the atmosphere.