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The International Conference on Multiphase Systems, ICMS'2000
Ufa, RUSSIA, June 15-17, 2000

Interaction of Sound and Ultrasound Waves in Bubbly Systems

Khismatullin D. B.

Department of Continuum Mechanics, Bashkir State University, Ufa, RUSSIA

Akhatov I. Sh.

Institute of Mechanics of R.A.S., Ufa, RUSSIA

The interaction of long-wave (sonic) and short-wave (ultrasonic) perturbations in a weakly compressible viscous liquid with gas bubbles is considered. It is shown that the equation describing dynamics of weak perturbations in a bubbly liquid allows the Benney-Zakharov long-wave / short-wave resonance. By the method of multiple scales the equations of one- and two-dimensional wave interaction are derived. Non-resonant, resonant and {\it degenerate} cases are discussed. The {\it degenerate} case is the specific of long-wave / short-wave interaction in a bubbly liquid. The 'degeneration' phenomenon consists in vanishing of the interaction coefficients at a certain frequency of the short wave. The conditions by which a two-dimensional sound--ultrasound interaction in bubbly mixtures leads to singular focusing of disturbances (blowup instability) are derived. The numerical investigations of degenerate resonant interaction between sound and ultrasound and of singular focusing of ultrasound in these media are done. The influence of dissipation on one- and two-dimensional wave interactions is analysed. The role of a long-wave / short-wave resonance in the propagation of two-dimensional disturbances is studied.