A Diagnosis of the Asymmetry in Top-Down and Bottom-Up Diffusion Using a Lagrangian Stochastic Model

Abstract

A Lagrangian stochastic model of particle trajectories is used to investigate the asymmetry in vertical diffusion from area sources at the bottom and top of an inhomogeneous turbulent boundary layer. Such an asymmetry was discovered in the large-eddy simulations (LES) of the convective boundary layer (CBL) by Wyngaard and Brost (1984) and Moeng and Wyngaard (1984). For inhomogeneous Gaussian turbulence, a diffusion asymmetry results from the vertical asymmetry in the vertical velocity variance about the midplane of the boundary layer. For small turbulence time scales, this is predictable from eddy-diffusion (K) theory. However, for large time scales, K theory is inapplicable as evidenced by countergradient flux regions and K singularities. The fundamental causes of the K model breakdown are the memory (large time scale) and vertical inhomogeneity of the turbulence, which lead to a mean vertical acceleration of particles away from the source and a ?drift? velocity. A positive skewness in vertical velocity enhances the drift velocity for a bottom source and suppresses it for a top source, thus leading to a greater diffusion asymmetry than in Gaussian turbulence; this is independent of the variance profile. The asymmetry due to skewness is caused by the bias in the probability density function of vertical velocity (w)?larger positive w values and smaller negative ones than in Gaussian turbulence. The results for inhomogeneous skewed turbulence are in good agreement with the LES results for the CBL.