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 multiple scales one- and two-dimensional nonlinear interaction equations are derived. The degeneracy of the interaction is found in bubbly fluids. This phenomenon lies in the fact that the interaction coefficients vanish at a certain frequency of ultrasound. We demonstrate that the integrable Davey–Stewartson I (DSI) system of equation can describe the two-dimensional sound-ultrasound evolution. The DSI equations are remarkable by their solutions referred to as dromions. In bubbly fluids the dromion represents the localized focused ultrasound wave which can alter the direction of its motion under changes in the boundary conditions for the sound wave. The condition of singular focusing of ultrasound in bubbly fluids is obtained. By numerical analysis of the interaction models, we reveal such processes as intensification of ultrasound by sound, nonlinear instability of a sound profile, and prove the validity of the singular focusing condition. Finally, possible applications of the results are outlined.