The Baroclinic, Variable Eddy Viscosity Ekman Layer

The WKB method is used in conjunction with the variation of parameters technique to find an approximate analytical solution for Ekman layers with eddy viscosity and horizontal pressure gradient that are each variable with height from the surface. Behaviour of the solution is illustrated by comparing model output when several eddy viscosity and horizontal pressure gradient profiles are used. Cases where the pressure gradient decreases with height accentuate the super-geostrophic peak in the wind velocity profile, with decreasing eddy viscosity with height further enhancing this effect. Increasing pressure gradient with height reduces or eliminates the peak. The model output when using an eddy viscosity that has a low-level peak fits marine boundary-layer data taken during ASTEX better than the classic solution - the model giving greater low-level mixing which is seen in ASTEX data as well as in data from ERICA.