Hostname: page-component-77c89778f8-5wvtr Total loading time: 0 Render date: 2024-07-22T07:20:41.616Z Has data issue: false hasContentIssue false
  • English
  • Français

Conserved quantities for axisymmetric cavities near boundaries

Published online by Cambridge University Press:  17 April 2009

R. Paull  and
J.R. Blake
R. Paull
Affiliation:
12 Marshall StreetKingston Qld 4114Australia
J.R. Blake
Affiliation:
Department of MathematicsThe University of WollongongWollongong NSW 2500Australia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 41 , Issue 2 , April 1990 , pp. 215 - 222
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Batchelor, G.K., An introduction to fluid dynamics (Cambridge University Press, Cambridge, 1967).Google Scholar
[2]Benjamin, T.B., ‘Hamiltonian theory for motions of bubbles in an infinite liquid’, J. Fluid Mech. 181 (1987), 349–379.CrossRefGoogle Scholar
[3]Benjamin, T.B. and Olver, P.J., ‘Hamiltonian structure, symmetries and conservation laws for water waves’, J. Fluid Mech. 125 (1983), 137–185.CrossRefGoogle Scholar
[4]Blake, J.R., ‘The Kelvin impulse: application to cavitation bubble dynamics’, J. Austral. Math. Soc. (Ser. B) 30 (1988), 127–146.CrossRefGoogle Scholar
[5]Blake, J.R. and Cerone, P., ‘A note on the impulse due to a vapour bubble near a boundary’, J. Austral. Math. Soc. (Ser. B) 23 (1982), 383–393.CrossRefGoogle Scholar
[6]Kucera, A. and Blake, J.R., ‘Approximate methods for modelling the growth and collapse of cavitation bubbles near boundaries’, Bull. Austral. Math. Soc. 41 (1990), 1–44.CrossRefGoogle Scholar
[7]Longuet-Higgins, M.S., ‘On integrals and invariants for inviscid, irrotational flow under gravity’, J. Fluid Mech. 134 (1983), 155–159.CrossRefGoogle Scholar
[8]Longuet-Higgins, M.S., ‘Some integral theorems relating to the oscillation of bubbles’, J. Fluid Mech. 204 (1989), 159–166.CrossRefGoogle Scholar