Instability of the Ekman Spiral with Applications to the Planetary Boundary Layers

Abstract

The Ekman spiral boundary layer occurs in rotating systems near boundary surfaces perpendicular to the rotation axis when the flow is slow compared to the speed of rotation. New results are presented for the instability of the Ekman layer with a free boundary and for shear‐flow instability in the presence of density stratification: (1) For the Ekman boundary layer caused by wind stress on a free water surface the critical Reynolds number is much less than for the case of flow over a smooth rigid boundary. An example of this instability from a laboratory experiment is presented. (2) For the free‐surface case the distortion of the basic Ekman flow by finite‐amplitude motion is very large. (3) With unstable density stratification either shear‐flow instability or thermal convection may dominate according to the relative values of Rayleigh and Reynolds numbers. (4) With stable density stratification the shear‐flow instability may be resonant with internal gravity‐wave oscillations so that damping of the cellular circulations is minimized. Some of the implications of these results for the planetary boundary layers of the atmosphere and ocean are considered.