Nonlinear internal resonance interaction between surface waves and internal waves in an inhomogeneous laminated liquid

Abstract

Eight nonlinear resonances may arise in a two-layer liquid with a free surface, as follows from asymptotic calculations of the second order of smallness. Two of them involve waves generated by either surface, and six mixed resonances involve waves generated by different surfaces. Of these six resonances, two are degenerate and the remaining four are secondary combination resonances. However, not all of them are observed in practice. In the mixed combination resonances, interaction arises only between surface waves provided that the internal wave (which does not change its parameters but is necessary for the resonance to occur) has a catalytic influence.