Evaluation of a Buoyancy and Shear Based Mixing Length for a Turbulence Scheme

We present a new diagnostic mixing length for a turbulence scheme based on a prognostic equation for the turbulence kinetic energy. The formulation adds a local vertical wind shear term to the non-local buoyancy-based mixing length currently used in the research mesoscale model Meso-NH. The combined effects better represent local mixing for stably stratified flows where the wind shear plays a major role. The proposed formulation is directly evaluated in large-eddy simulations of stable, neutral, and unstable atmospheres. It is tested in single-column simulations with different length scale formulations and compared to large-eddy simulations. Idealized cases with varying surface cooling rates and different prescribed geostrophic winds are used to evaluate the impact of the new model on the stable boundary layer. The model reduces the over-diffusion typically occuring in modeling the stable boundary layer and shows better performance in terms of the turbulent mixing, the temperature inversion, and the boundary-layer and low-level jet heights compared to large-eddy simulations. A slight improvement of the turbulence intensity is shown for convective boundary layers.