Abstract
The evolution of a cylindrical gaseous bubble produced by an underwater electrical discharge is considered in the present study. Both the gas flow inside and the water flow around the bubble are theoretically analyzed in a cylindrical coordinate system. By using the potential flow theory and multiple scale expansion method, governing equations of both flows and the bubble surface are formulated. The radial oscillation of the bubble surface is composed of a slow-changing equilibrium part and a fast-changing displacement. The former corresponds to a quiescent water domain and a uniform gas column, and the latter corresponds to acoustic waves in gas and water flows. The axial gas wave can evolve into a stable standing wave if the bubble length is multiples of half a wavelength. The internal acoustic standing wave then causes a synchronous small-amplitude oscillation of the bubble surface when the frequency of the acoustic wave is close to the natural frequency of the bubble surface. An underwater discharge experiment is implemented to validate our theory. Finally, a novel method to estimate the plasma pressure is proposed based on our theory.
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