К НЕЛИНЕЙНОЙ ДИНАМИКЕ ТУРБУЛЕНТНЫХ ТЕРМИКОВ

Abstract

Often used model of turbulent convection from localized sources of buoyancy and (or) momentum acting for a short time – isolated thermals. In such a model, the perturbation region (thermal) is approximately represented as a “bubble” or a vortex ring of variable volume and mass that rises (or descends depending on the perturbation sign). The volume of thermals is gradually increasing due to the capture of adjacent volumes of the environment (“entrainment”). The dynamics of a thermal is described by a nonlinear system of ordinary differential equations – the equations of balance of mass, momentum and buoyancy. In the present work, the nonlinear integral model of turbulent thermals is generalized to the case of the presence of horizontal components of its motion relative to the medium (for example, the emergence of a thermal in a shear flow). Compared to traditional models, the possibility of the presence in the thermal of volume heat and momentum sources is additionally taken into account. The problem is solved in quadratures. One of the possible applications is the artificial stimulation by local sources of impulse of downward movements in the atmosphere in order to influence convective clouds. The solution depends on nine parameters – stratification, vertical shear of the background current, intensities of the above-mentioned volume sources, initial conditions for the thermal radius, its buoyancy, and the three components of the thermal velocity. Different limiting cases are analyzed. Attention is paid to the nonlinear effect of the interaction of the horizontal and vertical components of the thermal motion, since each of the components affects the intensity of entrainment, i.e. on the growth rate of thermal dimensions and, consequently, on its mobility. Intensification of entrainment due to the interaction of a thermal with a transverse flow can lead to a significant decrease in its mobility. From this, in turn, depends on the degree of horizontal transfer of a thermal by a background current. Some limiting cases were previously analyzed in the author’s cited below. This study was supported by Program 56 of the Fundamental Research of the Presidium of the Russian Academy of Sciences.