Abstract
Motivated by recent laboratory and field observations, this paper reports the first quantitative measurements of the stabilization phase of interfacial instability in a two-layer fluid in surface wave motion. The instability results from the formation of a resonant triad between the surface wave and noise-level sub-harmonic interfacial waves. To exclude the effects of interfacial mixing on the interaction, the experiments were carried out with immiscible fluids. Carrying out a resonant interaction analysis to the third order of nonlinearity using a Lagrangian formulation, we also show for the first time that the three-wave resonance is inherently accompanied by a harmonic four-wave resonant interaction among the interfacial waves. Omitting the four-wave resonant interaction terms from the analysis results in over-prediction of the final amplitude of the interfacial waves by a factor greater than 2. The theoretical predictions are well-supported by the experiments.
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