Theoretical Investigation of a Double Family of Normal Modes in an Underwater Acoustic Surface Duct

This article investigates an underwater surface duct model that requires two distinct families of normal modes for the representation of the acoustic field in the image-interference region. Each family contains an infinite number of modes. In the image-interference region, the propagation losses of mode and ray theory give almost identical results, with the mode approach being limited at short ranges by the large number of modes required and by the necessity for extreme computational accuracy in determining the contributions of individual modes. By means of phase velocity, the first and second family of modes are associated with ray groups that, respectively, do or do not reflect from the ocean surface. A new method of identifying mode number by phase changes in the mode depth function is presented. The fallacy of the incoherent addition of modes at close range is illustrated. Mathematical techniques for determining eigenvalues are discussed in detail. The analysis of a number of limiting cases leads to explicit approximations that provide guides to the general theory that can be expressed only in complicated forms.