On the adiabatic normal modes in the 3-D inhomogeneous waveguide

Abstract

Several distinct formulations of the adiabatic approximation have been proposed in the literature on modal propagation in the 3-D, range-dependent waveguide. These formulations predict the same phase but differ in the adiabatic mode amplitude and, hence, in their reciprocity and energy-conserving properties. These formulations, including those due to L. M. Brekhovskikh and O. A. Godin [Acoustics of Layered Media. 2. Point Sources and Bounded Beams (Springer-Verlag, Berlin, 1992), p. 253] and M. B. Porter [J. Acoust. Soc. Am. 96, 1918–1921 (1994)], are compared with respect to their accuracy and domain of validity assuming small and smooth variation of mode propagation constants characteristic of underwater acoustic waveguides. Perturbation theory for horizontal (modal) rays and dynamic ray tracing are used in the analysis. A new approximate expression for the adiabatic mode amplitude in 3-D problems is derived that requires environmental information only along source–receiver radial and possess higher accuracy than previous formulations. The domain of validity of the result is determined in terms of horizontal gradients of environmental parameters. Mode phase corrections due to horizontal ray curvature are evaluated. Implications on applicability of the uncoupled azimuth approximation for sound propagation modeling in a horizontally inhomogeneous ocean are discussed. [Work supported by NSERC.]