Instability and diapycnal momentum transport in a double-diffusive, stratified shear layer

The linear stability of a double-diffusively stratified, inflectional shear flow is investigated. Double-diffusive stratification has little effect on shear instability except when the density ratio R-rho is close to unity. Double-diffusive instabilities have significant growth rates and can represent the fastest-growing mode even in the presence of inflectionally unstable shear with a low Richardson number. In the linear regime, background shear has no effect on double-diffusive modes except to select the orientation of the wave vector. The converse is not true: double-diffusive modes modify the mean shear via momentum fluxes. The momentum flux driven by salt sheets is parameterized in terms of a Schmidt number (ratio of eddy viscosity to saline diffusivity) Sc-s. In the oceanic parameter regime, Scs is less than unity and can be approximated as Sc-s = 0.08 ln[R-rho/(R-rho-1)]. Enhanced molecular dissipation by unstable motions is quantified in terms of the dissipation ratio Gamma, and the results are compared with observations. Corresponding results are given for diffusive convection in an inflectional shear flow, though linear theory is expected to give a less accurate description of this mechanism.