An Improved Ekman Layer Approximation for Smooth Eddy Diffusivity Profiles

The Ekman boundary-layer model is extended analytically for a gradually varying eddy diffusivity K(z) ≥ 0, z ≥ 0. A solution for the Ekman layer is provided having similar structure to the constant-K case; that is, exponentially decaying sine functions for the two horizontal wind components. The analytical asymptotic solution compares well with its numerical counterpart for various K(z). The result can be useful in theoretical studies such as Ekman pumping, for efficient estimation of the Ekman layer profiles in various analyses with near-neutral stratifications, or for a rapid initialization of mesoscale models.