Mode interactions in an isovelocity ocean of uniformly varying depth

Abstract

Pierce’s treatment of normal-mode propagation for an ocean in which physical parameters vary slowly with range is used to calculate mode interactions for isovelocity water of depth varying linearly with range. Simplifying assumptions are (a) two dimensions only, depth and range, and (b) a pressure-release bottom interface (reasonably valid for all but the highest modes). After general procedures are established, an explicit result is derived for the interaction contribution of mode 2 to mode 1 (the lowest mode), for down-slope propagation with several allowed modes. Changes, mainly only of signs and phases, are derived to cover up-slope propagation as well as the contributions of mode 1 to mode 2. Each interaction yields a forward-scattered component and a considerably weaker back-scattered one. Each is proportional to the bottom slope. The forward component is also proportional to the ratio depth to acoustic wavelength; the back component follows the inverse ratio. When normalized to the unperturbed outgoing mode functions, the interaction contributions are essentially of equal magnitudes, as would be expected in the absence of loss mechanisms.