Degree Name

Doctor of Philosophy


Department of Mathematics


The two principal phenomena associated with an underwater explosion are bubble motion and shock wave propagation. In this thesis both are investigated.

The study of bubble dynamics proceeds by assuming irrotational flow in incompressible and inviscid fluid. A technique is developed for the derivation equations of motion for a spherical bubble in flow domains of simple geometry.The concept of the Kelvin impulse is exploited in this endeavour. The model is used to infer the behaviour of bubbles that deform from spherical shape.

The boundary integral method is then employed to compute the motion of underwater explosion bubbles. The pressure within the bubble is assumed a function of the bubble volume and it is demonstrated that under some circumstances the increasing bubble pressure upon collapse will cause the non-bubble to rebound. In these cases the high speed liquid jets characteristic collapse are shown to grow during the rebound phase of the motion. Data for the behaviour of bubbles described by a wide range of the physical parameters governing the motion is presented.

The jet that forms upon collapse or rebound threads the bubble and ultimately impacts upon the far side of the bubble. To date, boundary integral methods have been unable to compute the motion beyond this time. Thus the impact considered and a boundary integral method is developed to compute the of the toroidal bubble that is created by this jet penetration. The dynamics of toroidal bubbles is then investigated.

The theory of geometrical shock dynamics is considered in the context of propagation of an underwater blast wave. The significant feature of such a wave is the non-uniform flow field behind the shock. In order to account for the propagation of a shock down a tube of slowly varying cross section is reconsidered. The solution of this problem is the basis for the theory of geometrical shock dynamics. It is found that the propagation is described by an infinite sequence of ordinary differential equations that can be closed by a process of truncation. Truncation at higher equations allows higher order derivatives of flow quantities evaluated at the shock to be included in the description of the shock motion. In this manner account may be taken of non-uniform flow conditions behind the shock. These equations are implemented in the numerical scheme of geometrical shock dynamics and the diffraction of an underwater blast wave is considered.