Interfacial mode interactions in horizontal gas—liquid flows

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Abstract
The behaviour of shear-generated interfacial waves in a cocurrent gas-liquid flow in a small rectangular channel is studied experimentally at conditions close to neutral stability. It is found that the linearly most unstable mode, which typically has a frequency of 8–10 Hz and a wavelength 1–4 cm, grows initially — followed immediately by the first overtone. Measurements of the bicoherence spectrum indicate that the overtone and fundamental are coherent in phase, which suggests that energy is transferred from the fundamental to the linearly stable first overtone. This energy transfer mechanism can stabilize the system, as evidenced by data, which shows that the first mode can saturate with a wave slope small as as 0.005. Theory based on weakly nonlinear mode-interaction equations suggests that this steady state should be stable at conditions close to neutral stability where only overtone modes are present. However, under more severe conditions, where the amplitude of the fundamental mode becomes sufficiently large, a subharmonic mode may be excited. The generation of the subharmonic, when it is linearly stable with respect to the flat film base state, can be interpreted as a linear instability of the steady state containing the fundamental and overtones. Modes that are sidebands (with wavenumbers = k ± δk) to the main peak may also occur. These can participate in interactions with low-frequency modes (i.e. δk) and thereby transfer energy to frequencies much below the fundamental. It is expected that all of these interactions play important roles in determining the wave spectrum of conditions far away from neutral stability.