Brownian ensemble of random-radius buoyancy vortices and Maxwell velocity distribution in a turbulent convective mixed-layer

Abstract

The stochastic ensemble of convective thermals (vortices), forming the fine structure of a turbulent convective atmospheric layer, is considered. The proposed ensemble model assumes all thermals in the mixed-layer to have the same determinate buoyancies and considers them as solid spheres of variable volumes. The values of radii and vertical velocities of the thermals are assumed random. The motion of the stochastic system of convective vortices is described by the nonlinear Langevin equation with a linear drift coefficient and a random force, whose structure is known for a system of Brownian particles. The probability density of the thermal ensemble in velocity phase space is shown to satisfy an associated K-form of the Fokker-Planck equation with variable coefficients. Maxwell velocity distribution of convective thermals is constructed as a steady-state solution of a simplified Fokker-Planck equation. The obtained Maxwell velocity distribution is shown to give a good approximation of experimental distributions in a turbulent convective mixed-layer.