Self-Similar Solutions of the Integral Model of the Transient Convective Plume

The paper gives a detailed analysis of the current state of an integral theory of convective plumes and isolated convective elements (thermals). According to the paper, the basis of the existing convective plumes models is the approach of the vertical boundary layer, which allows us to neglect the pressure force in the equation of motion. Most of the integrated model of isolated convective elements are using the approach of the fixed environment, it also allows us to ignore the effect of pressure. However, ignoring the pressure forces do not allow to fully take into account the interaction between convective plumes (or thermals) and the environment. This paper presents a modified integral equation of isolated convective lifting element that takes into account the force of pressure on the thermals from the downcast environment. The proposed equation is considered that rising convection element is spherical, and the downward movement of the environment is potential. These simplifying assumptions make it possible to calculate the force of pressure on the thermals, based on classical hydrodynamics of a nonviscous fluid. Based on the proposed equation of motion is obtained that one of the well-known model of convective plume may be modified by including the effect of pressure. It is shown that both the original and the modified model contain a class of self-similar solutions corresponding instantaneous, power and exponential heat sources. The numerical calculation results of the vertical velocity and buoyancy self-similar profiles carried out on a modified plume model indicate quite acceptable agreement as other hydrodynamic models, and with the existing experimental data.