An Approximate Analytical Solution For The Baroclinic And Variable Eddy Diffusivity Semi-Geostrophic Ekman Boundary Layer

Abstract

The WKB method has been used to develop an approximate solutionof the semi-geostrophic Ekman boundary layer with height-dependenteddy viscosity and a baroclinic pressure field. The approximate solutionretains the same simple form as the classical Ekman solution. Behavioursof the approximate solution are discussed for different eddy viscosityand the pressure systems. These features show that wind structure inthe semi-geostrophic Ekman boundary layer depends on the interactionbetween the inertial acceleration, variable eddy viscosity and baroclinicpressure gradient. Anticyclonic shear has an acceleration effect on theair motion in the boundary layer, while cyclonic shear has a decelerationeffect. Decreasing pressure gradient with height results in a super-geostrophicpeak in the wind speed profile, however the increasing pressure gradient withheight may remove the peak. Anticyclonic shear and decreasing the variableeddy viscosity with height has an enhanced effect on the peak.

Variable eddy viscosity and inertial acceleration has an important role in thedivergence and vorticity in the boundary layer and the vertical motion at the top of the boundary layer that is called Ekman pumping. Compared to the constanteddy viscosity case, the variable eddy diffusivity reduces the absolute value ofEkman pumping, especially in the case of eddy viscosity initially increasing with height. The difference in the Ekman pumping produced by different eddy diffusivity assumptions is intensified in anticyclonic flow and reduced in cyclonic flow.