A skewed meandering plume model for concentration statistics in the convective boundary layer

Abstract

The meandering plume technique, which assumes that the total plume dispersion can be split into independent meander and relative dispersion components, is especially suited for modelling concentration (fluctuation) statistics in the convective boundary layer (CBL) with its large-scale turbulent motions. We develop a simple and practical meandering plume model for CBL applications that accounts for the skewed and inhomogeneous turbulence characteristics of the convective flow. The meander component is derived from a one-particle Lagrangian stochastic dispersion model by requiring that the meander and relative dispersion components correctly balance the first two total dispersion moments. Balancing of the third total moment implies a skewed relative dispersion, for which a bi-Gaussian distribution is used. The relative dispersion variance is parameterised with an extended asymptotic formulation for travel times much smaller than the Lagrangian integral time scale. For large travel times, the relative dispersion variance approaches the total dispersion variance. The in-plume fluctuations in the relative coordinate system are accounted for via the gamma probability density function. Laboratory data and large-eddy simulation results on total, relative and meander spreads are used to examine the model parameterisations and results. A requirement of the meandering plume model, that it should give the same mean concentration distribution as that obtained by the one-particle Lagrangian approach, is virtually fulfilled. Comparison of the model predictions of the concentration fluctuation intensity with existing laboratory data highlights the important contribution of in-plume fluctuations, which are normally neglected in meandering plume models. The paper also describes limitations of the new model and indicates the scope for further refinements.