Nonlinear Dynamics of Turbulent Thermals in Shear Flow

Abstract

The nonlinear integral model of a turbulent thermal is extended to the case of the horizontal component of its motion relative to the medium (e.g., thermal floating-up in shear flow). In contrast to traditional models, the possibility of a heat source in the thermal is taken into account. For a piecewise constant vertical profile of the horizontal velocity of the medium and a constant vertical velocity shear, analytical solutions are obtained which describe different modes of dynamics of thermals. The nonlinear interaction between the horizontal and vertical components of thermal motion is studied because each of the components influences the rate of entrainment of the surrounding medium, i.e., the growth rate of the thermal size and, hence, its mobility. It is shown that the enhancement of the entrainment of the medium due to the interaction between the thermal and the cross flow can lead to a significant decrease in the mobility of the thermal.