Lagrangian Stochastic Analysis of Flux-Gradient Relationships in the Convective Boundary Layer

Abstract

A generalized Langevin model is used to conduct Lagrangian statistical simulations of turbulent dispersion in a shear-free convective boundary layer. This model more nearly realizes a well-mixed steady state than previous models. It is, therefore, less influenced by spurious concentration gradients and so is more appropriate for the analysis of flux-gradient relationships. For instantaneous area sources mean concentration predictions compare very favorably with convection tank data and with other modeling attempts. Diffusivities calculated for a near-surface source also agree very well with convection tank data and show substantial regions of countergradient flux. Calculations for other source heights also show regions of countergradient flux and confirm that the diffusivity is a strong function of source height. For continuous area sources model predictions are in excellent agreement with the results of large-eddy simulations. They show that there is a strong asymmetry between ?top-down? and ?bottom-up? dispersion processes and that the bottom-up process has a substantial region of countergradient flux in the upper half of the boundary layer. Calculations of the third-order moment w2c throw doubt on the validity of the flux-gradient relation used to parameterize this quantity in second-order modeling.