The Hydrodynamics of Spherical Cavities in the Neighborhood of a Rigid Plane

Citation

Green, Joseph Matthew (1957) The Hydrodynamics of Spherical Cavities in the Neighborhood of a Rigid Plane. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/3R56-N749. https://resolver.caltech.edu/CaltechETD:etd-07132004-143023

Abstract

The velocity potential in a perfect fluid is found for a sphere which is translating in a direction normal to a rigid plane and which is simultaneously undergoing a change in its radius. The solution of the problem is conveniently pursued in the bispherical coordinate system. The kinetic energy of the fluid is determined. The dynamics of the motion of the translating sphere of variable radius is then described in terms of a Lagrangian which is formed from the kinetic energy of the fluid field and from the potential energy of the spherical cavity. The general equations of motion are exhibited and are solved in two cases of physical interest where approximations may be applied: (1) the case of an air bubble undergoing small oscillations because of a time varying external pressure, and (2) the case of a cavitation bubble collapsing so rapidly that the translational velocity may be neglected. For the cases in which the dynamics of the problem are specifically determined, pressure effects on the rigid plane are expressed in terms of the dynamic variables of the cavity. It is suggested that these results will serve to aid in the further quantitative experimental investigation of cavitation damage. The most important functions are evaluated numerically and are presented in a series of tables.

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