This paper presents a theoretical study of sound propagation in an ocean-surface duct. It deals with several aspects of the theory from a point of view which has not heretofore been taken in the analyses of this problem. The model used to describe a duct assumes the ocean surface to be smooth and the square of the refractive index to be bilinear. Alternative representations of the sound field excited by a point source are derived, the two playing the most significant role in this paper being the residue series and the normal-mode representation. It is shown that the depth functions of the residue series do not form a complete set, as those of a normal-mode representation must, and that the normal-mode spectrum is continuous, rather than discrete. The completeness properties of the normal-mode functions are then utilized in a study of the energy-trapping capabilities of the duct. In this connection, virtual modes are introduced and shown to lead naturally to the derivation of a leakage coefficient characteristic of the exponential leakage of energy out of the duct with increasing range. In addition, a cutoff-frequency criterion, useful in determining when a surface duct can trap energy, is derived.
A general perturbation theory is presented which is valid for small surface waveheights and for acoustic wavelengths of the order of the ocean-surface correlation length. Formal solutions for the perturbed field are given and are specialized, to the second order of approximation, for the case of a random ocean surface. The scattering reduces the intensity of the carrier (source) signal and creates signal sidebands that are not in general symmetric in amplitude about the carrier. A pair of system functions for the signal sidebands is defined.
Subject Classification: 30.40, 30.30, 30.25; 20.15.
A perturbation procedure is applied, through the second order of approximation, to the three-dimensional problem of scattering of sound from a point source by a rough surface progressing in the wind direction over an isovelocity ocean. The results satisfy conservation of energy, in a ray-theoretic sense, and are uniformly valid throughout the field. At points in the region of surface-image interference (Lloyd’s-mirror region), the signal is shown to be strongly modulated. Results are presented which depict the power in the carrier and signal sidebands. The latter are not, in general, symmetric in amplitude about the carrier. However, it is demonstrated analytically that, on two specific planes in the field, the signal power spectrum is symmetric about the carrier.
Subject Classification: 30.40, 30.20, 30.25.
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