Oscillations of a cloud of bubbles of small and not so small amplitude

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Abstract
The oscillations and sound emission of a bubble cloud containing a large number of bubbles in a liquid are studied. Averaged equations are used to describe the behavior of the mixture. Two analytical models are used to describe the behavior of the bubble contents. The oscillations of small amplitude are calculated analytically, those of not so small amplitude numerically. It is shown that the frequency spectrum is determined mainly by the total volume of gas in the cloud. The efficiency of sound emission is determined also by the magnitude of the individual bubbles. The frequency spectrum of the emitted sound has a peak at a frequency much lower than the eigenfrequency of the individual bubbles. At higher amplitudes of the oscillations, very high pressures occur at the center of the cloud that strongly limit the numerical calculations.
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