A new expression is proposed for the population density spectrum of wind-generated bubbles in the sea based on measurements made by Johnson and Cooke [B. D. Johnson and R. C. Cooke, J. Geophys. Res. 84, 3761–3766 (1979)] and by Thorpe [S. A. Thorpe, Phil. Trans. R. Soc. London Ser. A 304, 155–210 (1982)]. The main departures from existing expressions are the narrowing of the radius spectrum with increasing depth and the conclusion from Thorpe’s data that the bubble density at the surface is proportional to the cube of the wind speed. For acoustic propagation at a given frequency, useful expressions for the resonant bubble radius, damping coefficient, the complex sound speed, attenuation, and the refraction spreading loss are presented. Predicted results for each of these parameters are calculated for frequencies of 0 Hz and from 1.25 to 40 kHz in octave steps. As frequency is increased, the dominant cause of loss changes from refraction to attenuation. For a wind speed of around 15 m/s, the transmission anomaly (attenuation plus refraction spreading losses) at high frequencies, for one-way horizontal transmission in the surface duct, is several bels if the source (or receiver) is adjacent to the actual sea surface, but falls to a few decibels if the transducer is 4 to 5 m below the surface. Results for the cumulative probability of transmission anomaly are shown for a typical case of vertical motion of an acoustic transducer. The accuracies of the more common approximations are also analyzed. The approximation that can cause the greatest error is that which ignores the (comparatively sharp) upward refraction of near-horizontal sound rays passing through the bubble layer, since the length of their path through the layer is significantly overestimated.
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Marshall V. Hall (1989) studied this question.