Dispersion of Small-Scale Shear Instabilities

Abstract

Small-scale (Kelvin-Helmholtz) shear instabilities usually display very little dispersion. However, investigations by Hazel reveal an anomalous modal structure when the length scales associated with the density and velocity gradients are sufficiently different. We examine this modal splitting, and discover two distinct families of small-scale waves. The mean phase velocities of the two families can be quite different. The result is of considerable interest in studies of nonlinear interactions among small-scale shear instabilities, since it greatly extends the phase speeds allowed to the resulting disturbances.