Derivation of model-consistent universal functions for second-order turbulence models and their implications on Lagrangian stochastic methods for thermally stratified atmospheric surface boundary layer flows

The aim of this paper is to provide a description of high-Reynolds-number thermally stratified surface-boundary-layer flows consistent with given turbulence models and to study their implications on Lagrangian stochastic approaches. The emphasis is first put on the relations between the selected turbulence models and the resulting universal functions used to describe the first- and second-order moments for temperature and velocity. To this end, a methodology for deriving model-consistent mean profiles that agrees with the Monin—Obukhov theory is presented. This methodology is based on the derivation of algebraic solutions for the thermal and dynamic second-order moments, and on an iterative resolution of the turbulent dissipation rate. With adequate models for the dissipation rate, it is shown that the derived universal functions for the first- and second-order moments retrieve the correct asymptotic behaviors for both the stable and unstable limits. Based on these formulations, the consequences on Lagrangian stochastic models are then investigated since the turbulent model corresponding to the Lagrangian description must be consistent with the one used in the moment approach. For example, when using wall-function formulations, we highlight the importance of applying an-elastic wall-boundary conditions for both velocity and thermal instantaneous properties. Finally, an application to the case of linear-source dispersion is analyzed in the frame of hybrid moment–probability density function methods. It is shown that these methods can adequately account for stability effects and that models of instantaneous thermal quantities have a great impact on both buoyant plume rise and dispersion.