Spectral spreading from surface bubble motion

At low frequencies, surface bubbles contribute to acoustic backscattering in aggregate, and the motion of these bubble masses causes spectral spreading of the acoustic signals. This motion of the bubbles entrained in the surface waves is used to obtain the power spectrum of a low-frequency surface-scattered signal at a low grazing angle. A spectral distribution of the deterministic surface drift, augmented by breaking wave crests, is developed for the wave frequency components that are actively breaking. This motion is combined with the random motion in a wave cycle to predict the spectral widths of low-angle backscattered sound. To permit comparisons with measured data, convolutions of these spectra with simple square pulses of various durations are performed