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An Ensemble of Brownian Particles and a Stochastic Description of a System of “Slow” Convective Thermals at Convection Level

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Abstract

A system of slow convective thermals is considered in a vicinity of convection level. It is shown that a system of spherical convective thermals of fixed radius can be described by a stochastic equation, which is practically identical to Langevin equation for an ensemble of classical Brownian particles. Under the proposed approach, it was shown that the mean vertical velocity of a system of thermals at the convection level is zero. A kinetic analogue of thermodynamic temperature, corresponding to the second moment of the vertical velocity, was shown to exist for a system of thermals. Moreover, the associated Fokker–Planck equation for the system of slow convective thermals has a stationary solution corresponding to generalized Maxwell distribution over vertical velocities. Numerical and field experiments convincingly show that the generalized Maxwell equations is in agreement with the results of calculations and atmospheric measurements.

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Funding

This study was carried out under research project 0147-2019-0001, state registration АААА-А18-118022090056-0).

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Authors and Affiliations

  1. Water Problems Institute, Russian Academy of Sciences, 117701, Moscow, Russia

    A. N. Vul’fson & O. O. Borodin

  2. National Research University Higher School of Economics, 101000, Moscow, Russia

    A. N. Vul’fson & D. O. Demin

Authors
  1. A. N. Vul’fson
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  2. O. O. Borodin
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  3. D. O. Demin
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Correspondence to A. N. Vul’fson, O. O. Borodin or D. O. Demin.

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Translated by G.Krichevets

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Vul’fson, A.N., Borodin, O.O. & Demin, D.O. An Ensemble of Brownian Particles and a Stochastic Description of a System of “Slow” Convective Thermals at Convection Level. Water Resour 49, 212–222 (2022). https://doi.org/10.1134/S0097807822020130

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  • DOI: https://doi.org/10.1134/S0097807822020130

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