The inviscid and viscous instability of an unbounded shear layer: Effect of surface tension, density, viscosity and velocity profile

Parallel flows constitute prototypical configurations in many important applications in industry such as atomization and spraying of liquid fuels. A full description and understanding of the inviscid and viscous instability of realistic velocity profiles in unbounded two-phase shear layers without restriction on the range of the physical parameters of the flow are yet to be accomplished.; The inviscid and viscous instability characteristics of unbounded parallel flows of two fluids with different viscosities and densities are extensively investigated by performing a full linear stability analysis. The effects of density and viscosity stratifications, surface tension, Reynolds number and velocity profile are determined. The neutral stability and the maximal growth rate for the instability modes are calculated for a wide range of flow parameters.; The inviscid instability is first studied for the piecewise-linear profile and the error-function profile. Apart from the stabilizing effect observed in most of the cases, surface tension is found to destabilize the neutrally-stable waves that exist when surface tension is absent. A mathematical explanation and a physical explanation are given. The piecewise-linear profile does not match the more realistic results obtained with the error-function profile in the short-wavelength range, especially in nonhomogeneous shear layers.; The viscous instability is then studied for the error-function profile. A numerical scheme which is efficiently capable of handling a broad range of flow configurations and parameters is developed. The inclusion of viscosity alters the inviscid perturbations and produces additional modes, most remarkably, the interfacial mode that arises at large wavenumbers. The coexistence of three distinct modes in gas-liquid systems is observed. The parameters that control the mode crossing between these modes are determined. Energy considerations and parametric properties are found to be efficient tools to identify the nature of the instability. A region of stable wavenumbers which forms an island of stability inside the neutral curves is observed.; A comparison between the inviscid and viscous results is performed. Inviscid theory is found to accurately predict the instability of homogeneous shear layers but significantly fail to match the results of viscous theory in important practical conditions when density and viscosity stratifications are present.