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