A Simple Mixing Length Formulation for the Eddy-Diffusivity Parameterization of Dry Convection

Abstract

In this paper a simple mixing length formulation for the eddy-diffusivityparameterization of dry convection is suggested. The new formulation relates the mixinglength to the square root of the turbulent kinetic energy (e) and a time scale (τ ):l = τ √e. To close the parameterization the time scale is calculated as a functionof the boundary-layer height (h) and the convective velocity scale (w*), τ ∝ h/w*. Thesimpler approach of a constant time scale is also studied. The simulation of a case of dry atmosphericconvection with a one-dimensional boundary-layer model shows that the model with the new formulationreproduces quite well the main properties of the convective boundary layer. In particular,the entrainment is realistically represented by the new mixing length, which has the advantage of naturallydecreasing with the turbulent kinetic energy. Sensitivity studies to the surface flux and the lapserate, in the context of a simplified situation, show the robustness of the new formulation.