On Calculation of Intense Descending Convection Above a “Cold Spot” on a Horizontal Surface

Abstract

The author presents results of theoretical assessments referring to the convection that appears above a "cold spot" on a horizontal surface. Consideration is given to the case of thermal inhomogeneities with a fairly large amplitude where one cannot restrict oneself to a linear approximation. An analog of the Rayleigh number proportional to the amplitude of the temperature deviation and to the cube of the horizontal scale of the thermal inhomogeneity is a dimensionless criterion. From simple physical considerations and the scaling analysis, the author has obtained explicit analytical expressions for the depth (height) of penetration of thermal perturbations into a medium and for the amplitudes of convection-velocity components. These results are in good agreement with the experimental data available in the literature. The Nusselt number is proportional to the analog of the Rayleigh number to power 1/5; here, from a comparison with the experimental results, it follows that the proportionality factor is of the order of unity. The influence of the convection in question on the transfer of a passive impurity has been determined.