Sound-ultrasound interaction in bubbly fluids: Theory and possible applications

The interaction between sound and ultrasound waves in a weakly compressible viscous liquid with gas bubbles is considered. Using the method of multipl e scales one- and two-dimensional nonlinear interaction equations are deriv ed. The degeneracy of the interaction is found in bubbly fluids. This pheno menon lies in the fact that the interaction coefficients vanish at a certai n frequency of ultrasound. We demonstrate that the integrable Davey-Stewart son I (DSI) system of equation can describe the two-dimensional sound-ultra sound evolution. The DSI equations are remarkable by their solutions referr ed to as dromions. In bubbly fluids the dromion represents the localized fo cused ultrasound wave which can alter the direction of its motion under cha nges in the boundary conditions for the sound wave. The condition of singul ar focusing of ultrasound in bubbly fluids is obtained. By numerical analys is of the interaction models, we reveal such processes as intensification o f ultrasound by sound, nonlinear instability of a sound profile, and prove the validity of the singular focusing condition. Finally, possible applicat ions of the results are outlined. (C) 2001 American Institute of Physics.