THE THEORETICAL DESCRIPTION OF WAVE-WAVE INTERACTIONS AS A NOISE SOURCE IN THE OCEAN

The historical development of the theory governing the generation of ULF ocean noise by random surface fluctuations is reviewed. Emphasis is directed at the intrinsic relation between the two main theories currently in vogue, the perturbation procedure and that using an integral procedure based on Lighthill's equation. The relative contributions to the underwater pressure field from the direct radiation of turbulent air motion and the interaction of surface waves is examined. It is shown that even though the direct radiation can approach or even exceed the contribution from wave interactions in the early stages of sea development, overall it is much smaller than the latter. The use of the perturbation expansion in the theoretical analysis of wave interactions at low frequencies is justified. An estimate of the contributions from wave interactions of different order shows that the spectral levels decrease rapidly with increasing order, an increase in the order from m to m + 1 (m greater-than-or-equal-to 2), resulting in a decrease in the spectral peak level by about 25 dB. At the same time the peak frequency shifts from m-sigma-p to (m + 1) sigma-p, where sigma-p is the peak frequency of the ocean wave spectrum. With the basic importance of the second-order wave-wave interactions in the generation of the noise field confirmed, the formulas currently used to describe this interaction are reexamined and extended to include other wave effects including the contributions of the inhomogeneous component. This leads finally to a more comprehensive expression for the wave-generated ULF noise spectrum.