Modal decomposition of fields in range-varying waveguides

Abstract

Numerical solutions to parabolic equations (PE) provide the total contribution to the field at each point on the computational grid. For some applications, it is instructive to examine the propagation of individual spectral components, particularly in range-dependent waveguides, where mode coupling can be important. This paper presents a novel method for decomposing a numerical PE field into its horizontal wavenumber spectrum. At a given range in a range-dependent waveguide, the PE field versus depth is provided as initial data to a PE model which is used to propagate the field in a range-independent waveguide characterized by the local environmental conditions at the range of the initial data. A Fourier transform of this propagated field yields the PE modal spectrum directly. Moreover, if the standard parabolic equation is used to propagate the field, then the PE modal spectrum can be postprocessed into the correct modal spectrum for the one-way wave equation [D. J. Thomson and D. H. Wood, J. Acoust. Soc. Am. 82, 224–232 (1987)]. A numerical example involving upslope propagation is used to illustrate the proposed spectral decomposition method.