Ансамбль броуновских частиц и стохастическое описание системы "медленных" конвективных термиков на уровне конвекции

Водные ресурсы. 2022. Т. 49. № 2. С. 184–195.

Vulfson A. N., Бородин О. О., Demin D.

A system of "slow" convective thermals in the vicinity of the convection level is considered. It is shown that a stochastic equation can be used to describe the motion of a system of spherical convective thermals of a fixed radius, which is almost identical to the Langevin equation for an ensemble of classical Brownian particles. Within the framework of the proposed approach, it is shown that the average vertical velocity of a system of thermals at the convection level is zero. It is found that for an ensemble of thermals there is a kinetic analogue of the thermodynamic temperature corresponding to the second moment of the vertical velocity. Moreover, the associated Fokker-Planck equation for a system of "slow" convective thermals has a stationary solution corresponding to the generalized Maxwell distribution over vertical velocities. Numerical and field experiments convincingly demonstrate the correspondence of the generalized Maxwell distribution to the results of calculations and the data of atmospheric measurements

Keywords: стохастический ансамбль конвективных термиков, распределение Максвелла по скоростям в ансамбле конвективных термиков, уравнение Ланжевена, уравнение Фокера-Планка