Further consideration of the waveguide propagation of ambient sound in the ocean-surface bubble layer

Abstract

Measurements of the ambient sound generated by breaking waves over the range 40–20 000 Hz reveal well-defined spectral peaks [D. M. Farmer and S. Vagle, J. Acoust. Soc. Am. 86, 1897–1908 (1989)], suggesting the modulation of the ambient sound by the waveguide formed by the ocean-surface bubbles. The measurements show that the sound-speed profile in such a waveguide may be modeled by an exponential form. The theory of the waveguide propagation of the ambient sound is considered. It is shown that the sound propagation in the ocean-surface waveguides bears analogy with that in the optical waveguides formed by diffusion and can be solved analytically in a simple form. The cutoff frequencies of such waveguides are determined by a simple equation that incorporates only the waveguide parameters. Theoretical predictions of the spectral peaks, which seem to be associated with the modal cutoff frequencies, are compared favorably to the observations. Moreover, the present results are compared to the previous theory base on the model of inverse square sound-speed profiles in great details. It is shown that, although the two profiles are almost the same shape in the cases considered here, the sound propagation in the two waveguides is rather different. It is shown that the normal-mode propagation in the inverse square model is very sensitive to both source and receiver positions in addition to the waveguide parameters, and different modes can overlap, thereby making data fitting difficult. On the other hand, in the exponential model, the sound spectral function depends mainly on the waveguide parameters, e.g., sound-speed anomaly at the surface and the e-folding depth. Therefore the distinct spectral peaks observed are a stable prediction from the exponential waveguide model. The simplicity and the stability of the results can help solve the inverse problem, that is, “given an observed distribution of spectral peaks, can the bubble distribution be inferred?”