An application of the Langevin equation for inhomogeneous conditions to dispersion in a convective boundary layer

Abstract

AbstractDispersion in one dimension is simulated by the Langevin equation dW = −(W/TL)dt + dμ, where W is the velocity of the particle (hypothetical fluid element), TL the Lagrangian time scale and dμ the random velocity increment induced by forces exerted by the turbulence on the particle during dt. The moments of dμ in the Langevin equation in inhomogeneous conditions can be determined, by requiring that for large times the density distribution of the particles is the same as that of the air. In our numerical experiment the Langevin equation with the above‐defined moments is applied to diffusion in the convective boundary layer. Profiles of the moments of the vertical turbulence velocities, U(z), n = 1, 2, 3, are based on measurements and scaled by convective scaling; TL is assumed constant. Particles are released at several heights, with an initial velocity distribution that has the same moments as the Eulerian turbulence velocity distribution at that height. At the boundaries reflection conditions are imposed. Our results are extensively compared with water‐tank experiments of Willis and Deardorff, wind‐tunnel experiments of Poreh and Cermak, field experiments by Briggs and a model of Baerentsen and Berkowicz. The mean height and variance of the particles, the concentration field as a function of down‐wind distance and height, and ground level concentrations are presented. They agree very well with observations of dispersion in the convective boundary layer.