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

A.N. Vulfson^a, b, O.O. Borodin^a, b
^aRussian Academy of Science Oil and Research Institute, ul. Gubkina 3, Moscow, 119333, Russian Federation
^bHSE University, 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/
Web of Science

000377714800002
Scopus

2-s2.0-84973125282
ADS NASA

2016PhyU...59..109V
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)

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Received: 20th, August 2015, revised: 30th, November 2015, accepted: 1st, December 2015

Оригинал: Вульфсон А Н, Бородин О О «Система конвективных термиков как обобщённый ансамбль броуновских частиц» УФН 186 113–124 (2016); DOI: 10.3367/UFNr.0186.201602a.0113

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