  We consider the genesis and dynamics of interfacial instability in gas-liquid
flows, using as a model the two-dimensional channel flow of a thin falling film
sheared by counter-current gas. The methodology is linear stability theory
(Orr-Sommerfeld analysis) together with direct numerical simulation of the
two-phase flow in the case of nonlinear disturbances. We investigate the
influence of three main flow parameters (density contrast between liquid and
gas, film thickness, pressure drop applied to drive the gas stream) on the
interfacial dynamics. Energy budget analyses based on the Orr-Sommerfeld theory
reveal various coexisting unstable modes (interfacial, shear, internal) in the
case of high density contrasts, which results in mode coalescence and mode
competition, but only one dynamically relevant unstable internal mode for low
density contrast. The same linear stability approach provides a quantitative
prediction for the onset of (partial) liquid flow reversal in terms of the gas
and liquid flow rates. A study of absolute and convective instability for low
density contrast shows that the system is absolutely unstable for all but two
narrow regions of the investigated parameter space. Direct numerical
simulations of the same system (low density contrast) show that linear theory
holds up remarkably well upon the onset of large-amplitude waves as well as the
existence of weakly nonlinear waves. In comparison, for high density contrasts
corresponding more closely to an air-water-type system, although the linear
stability theory is successful at determining the most-dominant features in the
interfacial wave dynamics at early-to-intermediate times, the short waves
selected by the linear theory undergo secondary instability and the wave train
is no longer regular but rather exhibits chaotic dynamics and eventually, wave
overturning.
