Low-frequency acoustic resonances from the axi-symmetrical bubble plume

Abstract

Experiments were performed on the sound from an axi-symmetric, conical bubble plume formed by a vertical freshwater jet as it plunges into a freshwater pool. The fluxes of air and water entering the pool were controlled during the experiments, and, outside the plume sound was monitored over the frequency band 0.1 to 1 kHz. Up to five non-uniformly spaced peaks were observed in the acoustic spectrum, associated with the coherent, collective oscillations of the bubbles within the plume. The biphasic bubbly medium behaves as a continuum, acting as a resonant, conical cavity beneath the jet. The eigenfrequencies scale inversely as the square-root of the jet velocity and the fourth root of the air entrainment ratio. A two-component, theoretical model for the eigenfrequencies involves a fluid-dynamics argument, which shows that the sound speed increases as the square-root of depth in the plume. This is incorporated into an acoustic analysis in which the wave equation is solved analytically, taking account of the cone-like geometry of the bubble plume cavity. The theoretical frequencies of the lowest-order longitudinal modes of the bubbly cavity are found to exhibit the same inverse-fractional power-law scalings as those observed in the experiments. [Research supported by ONR.]