Effect of dissipation on the interaction between long and short waves in bubbly liquids

Abstract

The interaction of long and short waves in a rarefied monodisperse mixture of a weakly compressible viscous liquid and gas bubbles is considered. For taking the dissipation effects into account an effective-viscosity scheme is used. Four cases of dissipation are distinguished, namely, strong, medium, weak, and very weak dissipation. In the cases of moderate, weak, and very weak dissipation the equations of resonance and non-resonance wave interaction are derived using the multiscale method. The effect of "degeneration" of the interaction is detected in certain of the models constructed. In the case of "degeneration" a class of new models of the dissipative resonance interaction is constructed and investigated numerically.