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

We investigate the linear stability of a double-diffusively stratified, inflectional shear flow. Double-diffusive stratification has little effect on shear instability except when the density ratio Rρ 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 low Richardson number. In the linear regime, background shear has no effect on double-diffusive modes except to select the orientation of the wavevector. The converse is not true: doublediffusive 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) Scs. In the oceanic parameter regime, Scs is less than unity and can be parameterized as Scs = 0.08 ln[Rρ/(Rρ−1)]. Enhanced molecular dissipation by unstable motions is quantified in terms of the dissipation ratio Γ, and the results 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.