The wind field in the nonlinear multilayer planetary boundary layer

Abstract

By use of the small parameter expansion method, the nonlinear planetary boundary layer (PBL) is studied in this paper. The PBL is divided into the surface layer and the Ekman layer, which is divided into several sublayers. In the surface-layer, the eddy coefficient K is taken as a linear function of height; in the Ekman layer, different constant K values are taken within different sublayers: these values are determined from O'Brien's formula (O'Brien, 1970) approximately. Under the upper and lower boundary conditions and the continuity conditions of the wind velocities and turbulent stresses at each boundary between sublayers, analytical expressions for wind velocity in all sublayers and the vertical velocity at the top of the PBL are obtained. A specific example of steady axisymmetrical circular high and low pressure areas is analysed, and some new conclusions are obtained. The results are in better agreement with reality than previous results. This example also shows that the vertical velocity at the top of the PBL caused by friction approaches zero near the center of a high or low pressure system for this model, but attains its maximum absolute values near the center of the high or low pressure area for Wu's (1984) model. This is due to the fact that in our model, the geostrophic wind speed near the center of this specific vortex approaches zero, which causes the wind shear and the friction effect to be very weak. Therefore the wind distribution in the PBL is very sensitive to the type of eddy coefficient.