Rays and local modes in a wedge-shaped ocean

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Abstract
Conventional normal mode theory cannot be applied to the nonseparable problem of wave propagation in an ocean with sloping bottom. For small bottom slopes, the sound field may be expressed approximately in terms of adiabatic modes, but this description fails when a mode propagating upslope passes through cutoff. An alternative solution by ray acoustics, valid at high frequencies, contains many multiply reflected contributions, and also undergoes difficult trapped to leaky ray transitions upslope. To address these transition problems, the conventional ray solution is used here as a convenient starting point for collective treatment of ray fields and their conversion into local modes. First, the ray fields are generalized by associating with each ray trajectory from source to observer a bundle of local plane waves that is multiply reflected between the boundaries and remains valid also in the transition regions. When the generalized ray series is subjected to Poisson summation and subsequent asymptotics on the transform integrals, it is found to furnish local modes which coincide with the conventional adiabatic modes where these exist. The local mode integrals also yield transition functions which smoothly continue an originally trapped adiabatic mode through cutoff to the leaky regime. The transition behavior agrees with that found by Pierce [J. Acoust. Soc. Am. 7 2, 523–531 (1982)] by an entirely different approach, and with that predicted by the spectral Green’s function method of Kamel and Felsen [J. Acoust. Soc. Am. 7 3 xxx–xxx (1983)]. The ultilization of rays and local modes in each step of the analysis here grants physical insight and therefore clarifies the mechanism of propagation in this range‐dependent environment.

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