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The Crushing of Air Cavities in a Liquid

Michael S. Longuet-Higgins
Proceedings: Mathematical and Physical Sciences
Vol. 439, No. 1907 (Dec. 8, 1992), pp. 611-626
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/52186
Page Count: 16
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The Crushing of Air Cavities in a Liquid
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Abstract

Although there is a growing amount of information on the distribution of bubble sizes in the upper layers of the ocean, no satisfactory theory for it has yet been given. In this paper we make a beginning with a theoretical model for the initial size distribution of bubbles generated by the shattering of a single air cavity, as in a breaking wave, when the bubbles are still close to the parent surface and before the distribution has been modified by buoyancy and convection. The expected size distribution depends upon the initial air volume and on the additional available energy. At small energies the probability density p(a) of bubble radii a is relatively narrow. At large energies the logarithmic distribution ap(a) tends to a certain unimodal form having a non-zero skewness. The width of the distribution at half its maximum is 2.16 octaves. Comparisons are made with both optical and acoustical measurements of the bubble size distributions from breaking waves in streams and in the ocean. A reasonable measure of agreement is found.

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