Secondary Kelvin–Helmholtz instability in weakly stratified shear flow

Abstract

The growth of secondary vortices on the braids separating Kelvin–Helmholtz billows is investigated via numerical simulations. The similarity theory of Corcos & Sherman (1976) is extended to include mixing processes with Prandtl number greater than unity, and is shown to provide a useful description of the physics of the braid regions just prior to the onset of secondary instability. The numerical study of Staquet (1995) is extended to include a wider range of Prandtl numbers and bulk Richardson numbers. Length and time scales of the secondary instability are compared with predictions based on normal-mode stability analysis of the braids. The onset of instability is shown to be accompanied by a dramatic increase in mixing efficiency in the braid region, emphasizing the potential importance of preturbulent Kelvin–Helmholtz billows for mixing stratified fluids.