On the determination of the height of the Ekman boundary layer

Abstract

The heighth _τ of the Ekman turbulent boundary layer determined by the momentum flux profile is estimated with the aid of considerations of similarity and an analysis of the dynamic equations. Asymptotic formulae have been obtained showing that, with increasing instability,h _τ increases as ¦μ¦^1/2 (where μ is the non-dimensional stratification parameter); with increasing stability, on the other hand,h decreases as μ^−1/2. For comparison, a simple estimate of the boundary-layer heighth _u determined by the velocity profile is given. As is shown, in unstable stratification,h _u behaves asymptotically as ¦μ¦⁻¹, i.e., in a manner entirely different from that ofh _τ.