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.