Long-wave-short-wave interaction in bubbly liquids

Abstract

The interaction of long and short waves in a rarefied monodisperse mixture of a weakly compressible liquid containing bubbles of gas is considered. It is shown that the equations describing the dynamics of the perturbations in the bubbly liquid admit of the existence of short-wave-long-wave Benney-Zakharov resonance. A special modification of the multiple-scale method is employed to derive the interaction equations. In the non-resonant case, the interaction equations reduce to the non-linear Schrödinger equation in the form of the short-wave envelope while, in the resonance case, they reduce to the well-known system of Zakharov equations. The characteristics of long-wave-short-wave interaction in a bubbly liquid lie in the fact that, at certain values of the frequency of the short wave, the interaction coefficients vanish (“interaction degeneracy”). A class of new interaction models is constructed in the case of “degeneracy”. Degenerate resonance interaction in a bubbly liquid is investigated numerically using these models.