Disturbance growth in two-fluid channel flow: The role of capillarity

This work examines the role of capillarity in the non-modal linear stability properties of three-dimensional disturbances in sheared two-layer flow of immiscible fluids of similar density. Capillarity reduces the transient growth of energy that occurs due to the non-normality of the linear stability problem according to a scaling of peak energy with We1/2 over a wide range of Weber number, viscosity ratio and wavenumber. More importantly, the participation of capillary modes in non-modal growth leads to oscillatory energy growth and to larger disturbance growth rates, features that are confirmed by computing the numerical range and numerical abscissa of the non-normal disturbance evolution operator. Examination of energy components and disturbance structure reveals that early rapid growth and subsequent oscillations are due to the coupling of streamwise vortices – the two-fluid analog of lift-up – to the displaced interface.