A semi-analytical model for mean concentration in a convective boundary layer

A model to predict the mean concentration field in convective conditions is proposed. This model is inspired by the probability density function (pdf) models, retaining their assumption of splitting a plume into updraft and a downdraft components. However, the proposed model is more flexible than the pdf models since it includes the effects of turbulence inhomogeneity and it can be adapted to non-stationary conditions. The formulation of the model ensures that in the limit of zero skewness a traditional Gaussian model is obtained. Thus, the model is applicable to conditions ranging from neutral to unstable. The model is solved numerically, but time consumption is negligible. Despite its simplicity, the model shows good performance compared to classical experiments and to more complex and physically consistent numerical models.