Convective-Region Top Front Propagation in a Uniform Medium under the Action of Point, Linear, and Plane Heat and Momentum Sources

Abstract

A relation between the height of a convective front rising in an unstratified medium and the momentum and heat fluxes released on the substrate surface is proposed for point, linear, and uniform plane sources arbitrarily dependent on time. This relation makes it possible to determine the integral power of a plume on the basis of optical observations of the height of the propagating convective front. As particular solutions, three classes of self-similar regimes related with the heat and momentum sources, whose rate is a step-shaped, power-law, or exponential function of time, are obtained. A one-dimensional integral model of a rising convective jet is constructed. The classes of self-similar jets corresponding to power or exponential heat and momentum sources are described. It is shown that all self-similar jets corresponding to heat and momentum sources governed by a power law with a fairly large exponent are characterized by the same temperature and velocity profiles.