Long-wave-short-wave interaction in bubbly liquids

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 i n the bubbly liquid admit of the existence of short-wave-long-wave Benney-Z akharov resonance. A special modification of the multiple-scale method is e mployed to derive the interaction equations. In the non-resonant case, the interaction equations reduce to the non-linear Schrodinger equation in the form of the short-wave envelope while, in the resonance case, they reduce t o 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 cer tain values of the frequency of the short wave, the interaction coefficient s vanish ("interaction degeneracy"). A class of new interaction models is c onstructed in the case of "degeneracy". Degenerate resonance interaction in a bubbly liquid is investigated numerically using these models. (C) 2000 E lsevier Science Ltd. All rights reserved.