On the nonlinear dynamics of turbulent thermals in shear flow

The nonlinear integral model of a turbulent thermal is extended to the case of the presence of a horizontal component of its motion with respect to the medium (for example, the rise of a thermal in shear flow). In contrast to traditional models, the possibility of heat release in the thermal is taken into account. For a piecewise constant vertical horizontal velocity profile medium and a constant vertical velocity shear, analytical solutions are obtained which describe different dynamic modes of thermals. The nonlinear interaction between the horizontal and vertical components of thermal motion because each of them influences the rate of entrainment of the ambient medium, i.e., the rate of increase in the size of the thermal and, hence, its mobility. It is shown that the enhancement of the entrainment of the medium due to the interaction of the thermal with the cross flow can lead to a significant decrease in the mobility of the thermal.