A probabilistic model for the noise generated by breaking waves

We present a probability law on both the noise field and the beam-noise time waveforms that is based on the assumption that the breaking-wave occurrences are described by a space-time Poisson process and that the breaking-wave waveforms are independent Gaussian processes. The probability law specifies the probability density of all orders in terms of its characteristic function, which is determined as a space-time integral of a functional involving the characteristic function of the contribution of an individual breaking wave. As an illustration, we present examples of the first-order probability density and the correlation function for a noise field observed on a vertical array operating in shallow water. It is seen that for the smaller elevation angles and for deep phones, where the energy is dominated by distant breaking waves, the observed noise waveforms are essentially Gaussian processes. Conversely, for beams pointed toward the surface and for shallow phones, where the noise is dominated by a small number of breaking waves, the noise wave forms are not Gaussian. Finally, we present a measure of the Gaussianity derived from an approximation to the characteristic function and apply it to identify the elevation angles and phone depths where the Gaussian approximation is not valid.