System of convective thermals as a generalized ensemble of Brownian particles

Physics-Uspekhi. 2016. Vol. 59. No. 2. P. 109–120.

Вульфсон А. Н., Borodin O. O.

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.

Ключевые слова: stochastic ensemble of convective thermals, Fokker-Planck equation, nonlinear Langevin equation, Maxwell velocity distribution for an ensemble of convective thermals