On the Nonlinear Dynamics of Turbulent Thermals in the Shear Flow

The known nonlinear integral model of a turbulent thermal is generalized to the case of the presence of the horizontal component of its motion relative to the surrounding medium (for example, the floating-up of a thermal in a shear flow). In addition, the possibility of the presence of a heat (buoyancy) source in a thermal is considered. In comparison with the author’s previous work, a solution is investigated for the case of unstable background stratification of the medium. The problem is solved in terms of quadratures. The asymptotics of the solution at large time intervals is analyzed. The solution describes, in particular, the nonlinear effect of the interaction of the horizontal and vertical components of the thermal motion, since each of the components affects the rate of entrainment of the surrounding medium, i. e., the growth rate of the thermal size and, hence, its mobility.