Three-dimensional convective and absolute instabilities in pressure-driven two-layer channel flow

A generalized linear stability analysis of three-dimensional disturbance in a pressure-driven two-layer channel flow, focusing on the range of parameters for which Squire's theorem does not exist is considered. Three-dimensional linear stability equations, in which both the spatial wavenumber and temporal frequency are complex, are derived and solved using an efficient spectral collocation method. A Briggs-type analysis is then carried out to delineate the boundaries between convective and absolute instabilities in m-Re space. We find that although three-dimensional disturbances are temporally more unstable than the two-dimensional disturbances, absolute modes of instability are most unstable for two-dimensional disturbances. An energy ``budget'' analysis also shows that the most dangerous modes are ``interfacial'' ones.