Adiabatic modes for up-slope propagation in a wedge-shaped ocean

Abstract

Recent numerical studies of upslope propagation in a wedge-shaped ocean with penetrable bottom [F. Jensen and W. Kuperman, J. Acoust. Soc. Am. 67, 1564–1566 (1980)], have revealed that intermode coupling is negligible for small bottom slopes but that each range-dependent adiabatic trapped mode field is strongly perturbed when that mode passes through cutoff. This observation has revived interest in extending the description of an adiabatic mode field through the transition region from trapped to radiating [A.D. Pierce, J. Acoust. Soc. Am. Suppl. 1 69, S69 (1981)]. We present a procedure of inherent general validity for range-dependent waveguides whereby an initial ray-acoustic field undergoing multiple reflection is converted into local mode fields by Poisson summation. Before the conversion, a plane-wave spectrum is fitted to the ray family, and the resulting Poisson-transformed spectral integrals, after asymptotic evaluation by the stationary phase method, are found to produce the conventional adiabatic trapped modes downslope from their cutoff points. As mode cutoff is approached, the simple stationary phase procedure must be modified, and the transformed spectral integrals become “canonical integrals” that trace the transition of a mode uniformly from the trapped to the radiating (leaky) regime. Results are shown for the transition function and its connection to the trapped and leaky mode fields downslope and upslope from the cutoff region. [Work supported by ONR Ocean Acoustics Branch.]