Temporal Stability of Boundary-Free Shear Flows: The Effects of Diffusion

Abstract:

The stability of boundary-free shear flow is studied for the case of variable viscosity due to binary diffusion across the shear layer. This leads to the main difficulty of this investigation, the direct coupling of the momentum and species equations in both the base state calculations as well as the stability analysis. Linear stability analysis is used to examine the effect of a nonuniform concentration profile on the stability of the flow. It is found that for the flow to be stable for all disturbance wave numbers the Reynolds number has to be zero. This is in agreement with constant viscosity free shear flow stability theory. Increasing the magnitude of concentration gradient (increasing the Schmidt number) destabilizes the flow.