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

References (65) Cited by (9) Similar articles (20) ↓

M.V. Kalashnik, M.V. Kurgansky, O.G. Chkhetiani “Baroclinic instability in geophysical fluid dynamics” 65 1039–1070 (2022)
K.V. Koshel, S.V. Prants “Chaotic advection in the ocean” 49 1151–1178 (2006)
O.G. Onishchenko, O.A. Pokhotelov et al “Structure and dynamics of concentrated mesoscale vortices in planetary atmospheres” 63 683–697 (2020)
B.M. Smirnov “Electrical cycle in the Earth’s atmosphere” 57 1041–1062 (2014)
O.G. Onishchenko, O.A. Pokhotelov, N.M. Astaf’eva “Generation of large-scale eddies and zonal winds in planetary atmospheres” 51 577–589 (2008)
V.M. Fedorov “Problems of parameterization of the radiation block in physical and mathematical climate models and the possibility of their solution” 66 914–930 (2023)
F.V. Dolzhanskii, V.A. Krymov, D.Yu. Manin “Stability and vortex structures of quasi-two-dimensional shear flows” 33 (7) 495–520 (1990)
L.Kh. Ingel, M.V. Kalashnik “Nontrivial features in the hydrodynamics of seawater and other stratified solutions” 55 356–381 (2012)
S.V. Bulanov, Ja.J. Wilkens et al “Laser ion acceleration for hadron therapy” 57 1149–1179 (2014)
D.N. Razdoburdin, V.V. Zhuravlev “Transient dynamics of perturbations in astrophysical disks” 58 1031–1058 (2015)
V.M. Fedorov “Earth insolation variation and its incorporation into physical and mathematical climate models” 62 32–45 (2019)
Yu.L. Klimontovich “Nonlinear Brownian motion” 37 737–766 (1994)
V.S. Anishchenko, A.B. Neiman et al “Stochastic resonance: noise-enhanced order” 42 7–36 (1999)
O.G. Bakunin “Stochastic instability and turbulent transport. Characteristic scales, increments, diffusion coefficients” 58 252–285 (2015)
I.R. Stakhovsky “Scale invariance of shallow seismicity and the prognostic signs of earthquakes” 60 472–489 (2017)
G.M. Zaslavskii, R.Z. Sagdeev et al “Minimal chaos, stochastic webs, and structures of quasicrystal symmetry” 31 887–915 (1988)
A.A. Chernyshov, K.V. Karelsky, A.S. Petrosyan “Subgrid-scale modeling for the study of compressible magnetohydrodynamic turbulence in space plasmas” 57 421–452 (2014)
M.Yu. Tretyakov, M.A. Koshelev et al “Water dimer and the atmospheric continuum” 57 1083–1098 (2014)
V.B. Efimov “Acoustic turbulence of second sound waves in superfluid helium” 61 929–951 (2018)
A.I. Zhakin “Electrohydrodynamics of charged surfaces” 56 141–163 (2013)

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