Wind, Waves, and Fronts: An Analytic Solution to the Generalized Ekman Model

The structure of shear flow in the boundary layers of the atmosphere and oceans is sensitive to a variety of parameters not included in classic Ekman theory, including the vertical structure of eddy viscosity, baroclinic pressure gradients, and surface waves. A variety of extensions to basic Ekman theory have been suggested to overcome these limitations, however analytic solutions are often available only for specific cases or forms of the parameters, with more general models requiring numerical solution. Here we present an approximate analytic solution to a generalized Ekman equation that includes the effects of vertically varying eddy viscosity, as well as any general inhomogeneous source of shear flow, such as might be associated with horizontal buoyancy gradients or the Coriolis-Stokes force. The approximate solution is shown to be accurate for a wide range of geophysically relevant parameters, while still maintaining a simple analytic form conducive to developing physical insight. Further, the solution extends smoothly to the equator, allowing application of this theory to studies of low-latitude boundary layers. Several observational data sets of near-surface ocean currents will be discussed in relation to the analytic solution, with a focus on the broad implications for Ekman transport, momentum flux, and boundary layer overturning circulations in the presence of wind stress, vertically varying eddy viscosity, horizontal buoyancy gradients, and surface waves.