A SIMPLE MIXING LENGTH FORMULATION FOR THE EDDY-DIFFUSIVITY PARAMETERIZATION OF DRY CONVECTION

摘要

In this paper a simple mixing length formulation for the eddy-diffusivity parameterization of dry convection is suggested. The new formulation relates the mixing length to the square rool of the turbulent kinetic energy (e) and a time scale (tau); l =tau e~(1/2). To close the parameterization the time scale is calculated as a function of the boundary-layer height (h) and the convective velocity scale (w_*)), tau propor. to /w*. The simpler approach of a constant time scale is also studied. The simulation of a case of dry atmospheric convection with a one-dimensional boundary-layer model shows that the model with the new formulation reproduces 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 naturally decreasing with the turbulent kinetic energy. Sensitivity studies to the surface flux and the lapse rate, in the context of a simplified situation, show the robustness of the new formulation.