Atmospheric Ekman Flows with Variable Eddy Viscosity

We revisit the classical problem of the behaviour of the wind in the steady atmospheric Ekman layer. We show, for general variable eddy viscosities, that in the Northern Hemisphere the time-averaged ageostrophic wind profile always decays in magnitude and turns clockwise with increasing height. This general result is new; all previous work is based on a few explicit, special examples. As part of the development, we present two ways of formulating the problem, one of which is a novel approach (making use of a transformation to polar coordinates) that helps to explain the complex nature of these flows. The two formulations are supported by several examples that show, for instance, how the deflection angle can be other than the familiar 45 ∘ . These results can be used as the basis for testing, and developing, various models for the height variation of eddy viscosity.