System of convective thermals as a generalized ensemble of Brownian particles

The system of thermals that makes the fine structure of a turbulent convective layer of a fluid is considered. A simplified probabilistic-geometrical approach is outlined that uses measurements along the observation line to determine the average in-plane parameters of the system. A dynamic equation for an isolated thermal interacting with its environment is derived. A Langevin equation similar to the stochastic equation for an ensemble of 'fast' Brownian particles is constructed for a system of thermals. The nonlinear Langevin equation for such a system leads to the associated kinetic form of the Fokker-Planck equation. It is shown that the stationary solution of the kinetic Fokker-Planck equation is identical to the Maxwell distribution and approximately consistent with the distributions measured in the turbulent convective layer of the atmosphere.