A new triad resonance in two-layer density stratified fluids

In a two-layer density stratified fluid it is known, due to Ball (1964), that two oppositely traveling surface waves may form a triad resonance with an interfacial wave. In the case of a real ocean with a relatively weak stratification, the two surface waves have close wavelengths and the resonant interfacial wave has the wavelength of about half of surface waves. Ball (1964) 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 obtains between two co-propagating surface waves (with close wavelengths) and a much longer interfacial wave. We present, via theoretical analysis and direct simulation, that for weak stratifications this new class of resonance results in a cascade of (near) resonance interaction that spreads the energy of initial waves to a number of lower and higher frequency waves. The resonance discussed here is in fact more likely to affect the evolution of a spectrum because waves within a typical spectrum are usually co-propagating than oppositely traveling. The significance of the resonance studied here is, particularly, more highlighted in the littoral zones, where the spectrum refracts toward a uni-directional wave train.