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Monopole emission of sound by asymmetric bubble oscillations. Part 2. An initial-value problem

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 Ave., La Jolla, CA 92037, USA Permanent address: Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge CB3 9EW, UK.
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Abstract

In Part 1 it was shown that an asymmetric, normal-mode bubble oscillation will emit monopole radiation at second order. Here we show that a general initial distortion of the bubble, with no initial volume change, can be resolved into normal modes each of which radiates independently. The zero-order ‘breathing mode’ is stimulated also.

Because of the peculiar damping characteristics, and the possibility of a resonance between the distortion modes and the breathing mode, the pulse of sound produced by the initial distortion will appear to have approximately the fequency of the breathing mode.

The conclusions are borne out in some detail by a comparison with the experiments of Fitzpatrick & Strasberg (1957) on the underwater sound generated by bubbles breaking away from a nozzle. A similar mechanism may contribute significantly to the generation of sound at the sea surface.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 201 , April 1989 , pp. 543 - 565
Copyright
© 1989 Cambridge University Press

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References

Banner, M. H. & Cato, D. H. 1987 Physical mechanisms of noise generation by breaking waves - a laboratory study. Proc. NATO Adv. Workshop on Natural Mechanisms of Surface Generated Noise in the Ocean, Lerici, Italy, 15-19 June 1987 In Sea Surface Sound (ed. B. R. Kerman), pp. 429–436. Reidel, 639 pp.
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Clarenden. 654 pp.
Devin, C. 1959 Survey of thermal, radiation and viscous damping of pulsating air bubbles in water. J. Acoust. Soc. Am. 31, 1654–1667.Google Scholar
Eller, A. I. 1970 Damping constants of pulsating bubbles. J. Acoust. Soc. Am. 47, 1469–1470.Google Scholar
Erdelyi, A., Magnus, W., Oberhettinger, F. & Tricomi, F. G. 1953 Higher Transcendental Functions, vol. 2. McGraw-Hill. 396 pp.
Farmer, D. M. 1987 Observations of high frequency ambient sound generated by air-sea interaction processes. Proc. NATO Adv. Workshop on Natural Mechanisms of Surface Generated Noise in the Ocean. Lerici, Italy, 15-19 June 1987 In Sea Surface ‘Sound (ed. B. R. Kerman), pp. 403–416. Reidel, 639 pp.
Farmer, D. M. & Vagle, S. 1988 On the determination of breaking surface wave distributions using ambient sound. J. Geophys. Res. 93, 3591–3600.Google Scholar
Fitzpatrick, H. M. & Strasberg, M. 1957 Hydrodynamic sources of sound. Proc. 1st Symp. on Naval Hydrodynamics, Washington, D.C., NAS-NRC Publ. 515, pp. 241–280. Washington, U.S. Govt. Printing Office.
Hollett, R. & Heitmeyer, R. 1987 Noise generation by bubbles formed in breaking waves. Proc. NATO Adv. Workshop on Natural Mechanisms of Surface Generated Noise in the Ocean, Lerici, Italy, 15-19 June 1987 In Sea Surface Sound (ed. B. R. Kerman), pp. 449–461. Reidel, 639 pp.
Kibblewhite, A. C. 1987 Ocean noise spectrum below 10 Hz - mechanism and measurements. Proc. NATO Adv. Workshop on Natural Mechanisms of Surface Generated Noise in the Ocean, Lerici, Italy, 15-19 June 1987 In Sea Surface Sound (ed. B. R. Kerman), pp. 337–360. Reidel, 639 pp.
Lamb, H. 1881 On the oscillations of a viscous spheroid. Proc. Lond. Math. Soc. 13, 51–66.Google Scholar
Lamb, H. 1932 Hydrodynamics, 6th edn. Cambridge University Press,632 pp.
Longuet-Higgins, M. S. 1950 A theory of the origin of microseisms. Phil. Trans. R. Soc. Lond. A243, 1–35.Google Scholar
Longuet-Higgins, M. S. 1953 Can sea waves cause microseisms? Proc. Symp. on Microseisms, Harriman, N.Y. Sept. 1952. NAS-NRC Publ. 306, pp. 74–93.
Longuet-Higgins, M. S. 1983 Bubbles, breaking waves and hyperbolic jets at a free surface. J. Fluid Mech. 127, 103–121.Google Scholar
Longuet-Higgins, M. S. 1988 Limiting forms for capillary-gravity waves. J. Fluid Mech. 194, 351–375.Google Scholar
Longuet-Higgins, M. S. 1989 Monopole emission of sound by asymmetric bubble oscillations. Part 1. Normal modes. J. Fluid Mech. 201, 525–541.Google Scholar
Prosperetti, A. 1977 Thermal effects and damping mechanisms in the forced radial oscillations of gas bubbles in fluids. J. Acoust. Soc. Am. 61, 17–27.Google Scholar
Toba, Y. 1961 Drop production by bursting of air bubbles on the sea surface (III). Study by use of a wind flume. Mem. Coll. Sci. Univ. Kyoto A29, 313–343.Google Scholar