Instabilities in a Stratified Fluid Having One Critical Level. Part III: Kelvin-Helmholtz Instabilities as Overreflected Waves

Abstract

We show that Kelvin-Helmholtz instabilities result from overreflected, vertically propagating, vorticity waves. Such waves exist in regions of large vorticity gradients. Just as with gravity wave instabilities, growth rates may be inferred from the quantization and overreflection of such waves. Moreover, overreflection concepts offer convenient insights into why Kelvin-Helmholtz instabilities, when they exist, tend to grow faster than gravity wave instabilities.