On the micropolar ekman problem

Abstract

Microfluid theory is applied to the classic Ekman problem. A general solution for the time dependent case is obtained. The characteristics of this solution are investigated by examining the complex response. Typically, the response is very similar to the complex response of the Ekman solution, thus suggesting that there is an equivalent Ekman time response for nearly any set of micropolar parameters. It is shown that for the steady state case, the two solutions exhibit significantly different features. With inhomogeneous boundary conditions for the gyration, the micropolar solution can produce a velocity profile that is virtually logarithmic with height near the lower boundary but which merges into a spiral Ekman-like layer and then finally into geostrophic flow. This profile is very similar to solutions obtained in studies of the atmospheric planetary layer which piece together boundary layer and Ekman layer solutions. Conceptually, the micropolar solution is much simpler in that an eddy viscosity which is an empirical function of height is not required.