The natural reference wavenumber for parabolic approximations in ocean acoustics (Q1067924)

A natural definition of the reference wavenumber \(k_ 0\) that appears in almost all underwater sound formulations based on a parabolic approximation emerges from Rayleigh's principle for progressive waves: the integrals over the depth of the kinetic- and potential-energy densities are equal. A formulation using this definition conforms to and refines \textit{R. M. Fitzgerald}'s suggestion [J. Acoust. Soc. Am. 57, 839- 842 (1975; Zbl 0319.76056)] that when the field is a sum of guided modes, the selected \(k_ 0\) should be a weighted average of the wavenumbers for the excited modes.