Maxwell Velocity Distribution for a Stochastic Ensemble of Thermals in a Turbulent Convective Mixed-Layer: Kinetic Approach

In this paper, we develop a stochastic model of an ensemble of convective eddies that produces an equilibrium velocity distri- bution of thermals. In the model, mixed-layer thermals are assumed to possess identical buoyancy and are considered as rigid balls of constant radii. The motion of an ensemble of convective eddies is described using a Langevin equation with a nonlin- ear dissipative force and a random force whose structure is known for an ensemble of Brownian particles. It is shown that the probability density of an ensemble of thermals satisfies the K-form of the kinetic Fokker-Planck equation with variable coeffi- cients. The Maxwell equilibrium velocity distribution of convective thermals is constructed as a stationary solution of the Fokker-Planck equation. It is shown that the Maxwell velocity distribution well approximates experimental distributions in the turbulent convective mixed-layer.