The subharmonic oscillations and combination-frequency subharmonic emissions from a resonant bubble: Their properties and generation mechanisms

Sizing bubbles using a two frequency technique which examines the coupling of a resonant subharmonic oscillation to an imaging beam is not prone to some of the inaccuracies and ambiguities of other methods. This combination frequency subharmonic signal is parametric in nature, and the amplitude onset threshold has been quantified for thirty tethered air bubbles in water. This paper details work which aims to investigate the generation mechanism of a bubble's subharmonic oscillations, and presents results from theoretical consideration of three potential mechanisms: (i) The possibility that at high amplitudes a bifurcation appears in a bubble's volumetric pulsations; (ii) the potential for bubbles driven at twice their resonant frequency to pulsate with a component at their resonant frequency (which is a subharmonic of the driving field); (iii) that surface waves are responsible. The first two mechanisms are examined using a numerical solution to the Gilmore-Akulichev model, and the third using plane surface theory. Whilst all three mechanisms show the potential far generating subharmonic oscillations, the first two demonstrate onset thresholds four and three orders of magnitude higher than the experimental threshold respectively. However, the threshold predicted using surface wave theory shows very good agreement with the experimental results.