Effect of miscibility on the linear instability of two-fluid channel flow

This study provides an extension into the finite-miscibility regime of theories for interfacial instabilities in two-fluid channel flow. When the two fluids are of high mass diffusivity, a new mode of instability, called here the overlap mode, appears when the critical layer of the dominant disturbance overlaps the viscosity-stratified layer. For poor diffusivity, the instability is qualitatively different: broadband and at low Reynolds number, beginning to resemble the Yih mode for immiscible interfaces. The results lend themselves to verification by experiment and direct numerical simulation.