  Most idealized studies of stratified shear instabilities assume that the
shear interface and the buoyancy interface are coincident. We discuss the role
of asymmetry on the evolution of shear instabilities. Using linear stability
theory and direct numerical simulations, we show that asymmetric shear
instabilities exhibit features of both Holmboe and Kelvin-Helmholtz (KH)
instabilities, and develop a framework to determine whether the instabilities
are more Holmboe-like or more KH-like. Further, the asymmetric instabilities
produce asymmetric mixing that exhibits features of both overturning and
scouring flows and that tends to realign the shear and buoyancy interfaces. In
all but the symmetric KH simulations, we observe a collapse in the distribution
of gradient Richardson number ($Ri_g$), suggesting that asymmetry reduces the
parameter dependence of KH-driven mixing events. The observed dependence of the
turbulent dynamics on small-scale details of the shear and stratification has
important implications for the interpretation of oceanographic data.
