A new triad resonance between co-propagating surface and interfacial waves

Abstract

AbstractIn a two-layer density-stratified fluid it is known, due to Ball (J. Fluid Mech., vol. 19, 1964, p. 465), that two oppositely travelling surface waves may form a triad resonance with an interfacial wave. Ball claims ‘there are no other interactions’ between two surface waves and one interfacial wave. Contrary to this, here we present a new class of triad resonance that occurs between two co-propagating surface waves and one interfacial wave. While in Ball’s resonance the interfacial wave has a wavelength of about half of two surface waves, in the new resonance presented here the interfacial wave has a much higher wavelength compared to those of surface waves. This, together with the unidirectionality of the participant triplet, makes the realization of the new resonance more likely in real ocean scenarios. We further show, via theoretical analysis and direct simulation, that, unique to this new class of resonance, the triad inevitably undergoes a cascade of (near-) resonance interaction that spreads the energy of initial waves to a number of lower and higher harmonics. The significance of the resonance studied here is, particularly, more emphasized in the littoral zones, where the spectrum refracts toward a unidirectional wave train.