The system of convective thermals as a generalized ensemble of Brownian particles

A.N. Vulfson^{ a, b},
O.O. Borodin^{ a, b} ^{a }Russian Academy of Science Oil and Research Institute, ul. Gubkina 3, Moscow, 119333, Russian Federation ^{b }National Research University Higher School of Economics, ul. Myasnitskaya 20, Moscow, 101000, Russian Federation

The system of thermals that makes the fine structure of a turbulent convective layer of liquid or gas is considered. A simplified probabilistic-geometrical approach is outlined that uses measurements along the observation line to determine the average in-plane parameters of this 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.

Keywords: stochastic ensemble of convective thermals, the nonlinear Langevin equation, Fokker—Planck equation, Maxwell velocity distribution for an ensemble of convective thermals PACS:05.10.Gg, 05.40.Jc, 44.25.+f, 92.60.Fm, 92.60.hk (all) DOI:10.3367/UFNe.0186.201602a.0113 URL: https://ufn.ru/en/articles/2016/2/b/ Citation: Vulfson A N, Borodin O O "The system of convective thermals as a generalized ensemble of Brownian particles" Phys. Usp.59 109–120 (2016)