On the Instability of Helmholtz Velocity Profiles in Stably Stratified Fluids When a Lower Boundary is Present

We investigate the stability of a Helmholtz velocity profile in a stably stratified fluid when a lower boundary is present. In addition to the traditional Kelvin-Helmholtz interfacial instability we find an infinitude of unstable internal gravity waves, the most unstable of which bear a close resemblance to disturbances observed in connection with clear air turbulence. It is shown that the gravity wave instabilities result from the ability of an unstable shear layer to overreflect such waves (reflected amplitudes are greater than incident amplitudes). Overreflection at the shear layer is constantly fed by total reflection from the lower boundary. The growth rate of gravity wave instabilities depends markedly on the distance between the shear layer and the ground. A mechanism is suggested whereby gravity wave instability can lead to long-lived almost neutral shear layers.