Conserved quantities for axisymmetric cavities near boundaries

Abstract

In axisymmetric irrotational flows of a perfect fluid under gravity there are three basic conserved quantities; axial momentum, energy and a circulation based, radial moment of momentum. This paper adapts these conservation principles to describe cavity collapse adjacent to a rigid boundary in a semi-infinite perfect fluid. They afford a global model accounting for volume change, migration and jet formation; physically the most significant features of bubble collapse close to a rigid boundary.