Vorticity, Divergence, and Vertical Velocity in a Baroclinic Boundary Layer with a Linear Variation of the Geostrophic Wind

The Ekman-Taylor problem for the planetary boundary layer is solved in the case of a thermal wind which varies linearly with height. The upper boundary condition is a vanishing ageostrophic wind, while the lower boundary condition is continuity of the stress vector across the interface between the planetary boundary layer and the surface layer. The latter condition is used to determine the magnitude and the direction of the wind at the bottom of the Ekman layer. Theoretical hodographs are compared with observed hodographs based on five years of ohservations from Ship N in the Pacific, giving fair agreement. The divergence, the vorticity, and the vertical velocity are calculated through the Ekman layer with emphasis on differences between the classical barotropic and the baroclinic cases; these differences are significant, especially in the vertical velocities as compared to the standard approximation. An extension of the present study to include thermal stratification is desirable.