Inviscid instability of an unbounded shear layer: effect of surface tension, density and velocity profile

Abstract

The inviscid temporal stability analysis of an unbounded shear layer of two fluids of different density is investigated. Two background velocity profiles are considered: the piecewise-linear profile and the more realistic error-function profile. The disturbance kinetic energy is analyzed to physically understand the mechanism that causes instability. The surface-tension effect is investigated extensively. Surface tension is found to destabilize the neutrally stable waves that exist when surface tension is absent. This surface-tension-induced unstable mode is generally weaker than the dominant mode and extremely less evident when the density and/or viscosity difference increases. Short-wavelength instability is observed with a background viscosity jump at the interface. A comparison between the two velocity profiles is presented. 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-layer flows; however, the phase-speed results are in a good agreement with those of the error-function profile.