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