Resolvent formulation of the Green's function for a wedge-shaped ocean

Abstract

By the method of resolvents or characteristic Green's functions [L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (Prentice-Hall, Englewood Cliffs, N J, 1973), Chap. 3], one may construct general contour integral representations of Green's functions for separable range-independent and range-dependent ocean profiles. From these general integral representations, one may derive a variety of alternative sound field representations, including those involving normal (discrete and continuous) modes, leaky modes, conventional and generalized rays, hybrid ray-mode combinations, etc. The method cannot be applied rigorously to nonseparable problems such as a wedge-shaped ocean with penetrable bottom. However, for small bottom slopes, we have managed to construct an approximate characteristic Green's function integral based on the ray-cycle invariant and on the requirement that the resulting normal mode representation arising from residues at the resonance poles yields the properly normalized and symmetrized trapped adiabatic modes downslope from their cutoff points. For upslope propagation, as a mode approaches cutoff, its resonance pole approaches a branch point and therefore couples strongly to its radiation field. In this transition region, the Green's function may be reduced asymptotically to a canonical integral which is discussed in detail. Beyond the transition region, the previously trapped mode pole becomes a leaky mode pole. The resulting formulation is compared with recent results obtained by other techniques (A.D. Pierce, J. Acoust. Soc. Am., to be published; J. M. Arnold and L. B. Felsen, this meeting). It is also shown how ray, ray-mode, and other relevant field representations can be obtained from the original integral. [Work supported by ONR Ocean Acoustics Branch.]