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Some integral theorems relating to the oscillations of bubbles

  • Michael S. Longuet-Higgins (a1)

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.

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Benjamin, T. B.: 1987 Hamiltonian theory for motions of bubbles in an infinite liquid. J. Fluid Mech. 181, 349379.
Benjamin, T. B.: 1989 Note on shape oscillations of bubbles. J. Fluid Mech. 203, 419424.
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, 155159.
Longuet-Higgins, M. S.: 1989a Monopole emission of sound by asymmetric bubble oscillations. I. Normal modes. J. Fluid Mech. 201, 525541.
Longuet-Higgins, M. S.: 1989b Monopole emission of sound by asymmetric bubble oscillations. II. An initial-value problem. J. Fluid Mech. 201, 543565.
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, 126.
Longuet-Higgins, M. S. & Ursell, F. 1948 Sea waves and microseisms. Nature 162, 700701.
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Some integral theorems relating to the oscillations of bubbles

  • Michael S. Longuet-Higgins (a1)

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