Journal of Fluid Mechanics

Monopole emission of sound by asymmetric bubble oscillations. Part 1. Normal modes

Michael S.  Longuet-Higgins a1p1
a1 Center for Studies of Nonlinear Dynamics, La Jolla Institute, 7855 Fay Ave., La Jolla, CA 92037, USA

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On a linearized theory, the pressure field due to bubbles oscillating asymmetrically in a ‘distortion mode’ decays with radial distance r like r−(n+1), where n > 1. Hence these modes have been thought to produce a negligible emission of sound. In this paper it is shown that, on the contrary, in nonlinear theory the distortion modes produce a monopole radiation of sound (n=0) at second order. Its frequency is twice the basic frequency of the distortion mode, and the sound amplitude is proportional to the square of the distortion amplitude. The magnitude of the pressure fluctuations within the bubble is comparable with 1 atmosphere.

(Published Online April 26 2006)
(Received June 16 1988)
(Revised September 30 1988)

p1 Permanent address: Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge CB3 9EW, UK