Stabilization mechanisms of short waves in stratified gas–liquid flow

Abstract

Interfacial waves grow in a cocurrent, stratified gas–liquid flow by extracting energy from the main flow. The most unstable mode typically has a wavelength comparable to or less than the liquid depth. Experiments show that these short waves can saturate at small amplitude with no generation of long-wave or transverse modes. By decomposing the typical Stuart–Landau analysis into three components, it is found that saturation usually occurs by cubic self-interaction of the fundamental mode but quadratic resonant interaction with the first overtone is also possible. Interaction with mean flow modes is usually much less important. Experiments confirm the predictions of weakly nonlinear theory. The measured overtone is found to be O(|A1|2) and is phase-locked with the fundamental except near a 1–2 resonance point where the fundamental and the overtone have comparable speeds. Near this resonance, the amplitudes are of the same order and the phase angle between them is observed to jump irregularly as predicted by modern dynamical systems theory for intermittent chaos near a heteroclinic cycle. The phase and magnitude of the overtone interaction specify the shape, chaotic dynamics and symmetry of the waves across resonance which are analyzed and confirmed experimentally.