Instability of the Stratified Ekman Boundary Layer and the Generation of Internal Waves

Abstract

With stable density stratification the shear-flow instability of the Ekman boundary layer exhibits two distinct regimes. At low values of a Richardson number the growth rate of instability, at specified Reynolds number, wavelength and angle, decreases linearly with Ri. At higher values of Ri the growth rate may decrease more slowly or may increase with Ri. The peculiar effects at the large values of Ri are interpreted as a resonance of the shear-flow instability with internal gravity waves. This resonance occurs when the speed of the shear-flow instability relative to the basic flow lies within the range of speeds of internal gravity waves relative to the basic flow, as determined by the Brunt-Väisälä frequency. Under these conditions the growth of waves appears to be dominated by the Type II mechanism of energy exchange for Ekman layer instability. Internal gravity waves generated by the shear-flow instability have their crests nearly parallel to the geostrophic flow above the boundary layer and move to the left of the geostrophic flow with speeds between approximately 0. 15 and 0.7 times the geostrophic speed. The type II energy exchange mechanism with the apparent resonance is permitted by the Coriolis forces.