Multiple Master Length Scales Derived from a Statistical Diffusion Theory

Abstract

The second-order closure models have been claimed to be one of the most appropriated tools to simulate numerically the planetary boundary layer. They reconcile the numerical amenability with a more basic physical description of the turbulent process. Several second-order closure models simulate appropriately the convective boundary layer(CBL). Simulating the stable planetary boundary layer(SBL) on the basis of a second-order closure model is a more difficult task. This certainly explains why SBL has been numerically simulated less frequently than the corresponding CBL(Moeng and Wyngaard,1989). The worst difficulty has to do with the proper choice of a turbulent master length scale(Mellor and Yamada,1982) that leads to an adequate parameterization of the undetermined terms in the equations for evolution of the second-order moments. In the SBL turbulence length scales are also relatively small and limited ultimately by the local Obukhov length rather than SBL Depth H. Recently Lacser and Arya(1986) have shown that the schemes which incorporate the local Monin-Obukhov length as a stability limit on the turbulent master length scale predict shallower and more stable boundary layers. Detailed comparisons between model predictions and data from the Cabauw mast have shown that Delage’s(1974) mixing-length formulation performed better than the other schemes in describing vertical profiles and temporal behavior of the mean and turbulent variables.