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Experimental and theoretical investigation of cubic stabilization of instability of an interface in surface wave motion

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.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.