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Some integral theorems relating to the oscillations of bubbles

Published online by Cambridge University Press:  26 April 2006

Michael S. Longuet-Higgins
Michael S. Longuet-Higgins
Affiliation:
Center for Studies of Nonlinear Dynamics, La Jolla Institute, 7855 Fay Avenue, Suite 320, La Jolla, CA 92037, USA
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Abstract

Two integral theorems are proved which are applicable to the motion of an incompressible fluid in three dimensions. From either of these theorems one can derive the monopole component of the pressure fluctuation at infinity when a bubble undergoes non-spherical oscillations. The results confirm and generalize some recent calculations of this effect (Longuet-Higgins 1989a). They also provide a basis for a physical discussion of the origin of the monopole terms.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 204 , July 1989 , pp. 159 - 166
Copyright
© 1989 Cambridge University Press

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References

Benjamin, T. B.: 1987 Hamiltonian theory for motions of bubbles in an infinite liquid. J. Fluid Mech. 181, 349–379.Google Scholar
Benjamin, T. B.: 1989 Note on shape oscillations of bubbles. J. Fluid Mech. 203, 419–424.Google Scholar
Lamb, H.: 1932 Hydrodynamics, 6th edn. Cambridge University Press, 632 pp.
Longuet-Higgins, M. S.: 1983 On integrals and invariants for inviscid, irrotational flow under gravity. J. Fluid Mech. 134, 155–159.Google Scholar
Longuet-Higgins, M. S.: 1989a Monopole emission of sound by asymmetric bubble oscillations. I. Normal modes. J. Fluid Mech. 201, 525–541.Google Scholar
Longuet-Higgins, M. S.: 1989b Monopole emission of sound by asymmetric bubble oscillations. II. An initial-value problem. J. Fluid Mech. 201, 543–565.Google Scholar
Longuet-Higgins, M. S. & Cokelet, E. D. 1976 The deformation of steep surface waves. I. A numerical method of computation. Proc. R. Soc. Lond. A 350, 1–26.Google Scholar
Longuet-Higgins, M. S. & Ursell, F. 1948 Sea waves and microseisms. Nature 162, 700–701.Google Scholar