Intrinsic modes: Numerical implementation in a wedge-shaped ocean

Abstract

Two recently developed related spectral theories [Kamel and Felsen, J. Acoust. Soc. Am. 73, 1120–2230 (1983); Arnold and Felsen, J. Acoust. Soc. Am. 73, 1105–1119 (1983)] have provided potentially new options for calculating source-excited sound fields in a weakly range dependent ocean environment. So far, these theories have been applied to a homogeneous two-dimensional ocean and bottom separated by a plane sloping interface. It has been recognized that their common building blocks are what have been referred to as ‘‘intrinsic modes’’ [Arnold and Felsen, J. Acoust. Soc. Am. 76, 850–860 (1984)]. Intrinsic modes have spectral integral representations that reduce in a lowest order approximation to adiabatic modes, where these can be defined, but which remain uniformly valid in their integral form through the cutoff transition in upslope propagation. An efficient numerical algorithm has now been developed for calculating the intrinsic modes and the Green’s function in the ocean and in the bottom. Numerical results are compared with those from the parabolic equation [Jensen and Kuperman, J. Acoust. Soc. Am. 67, 1564–1566 (1980)] and the augmented adiabatic mode theory [Pierce, J. Acoust. Soc. Am. 74, 1837–1847 (1983)]. Also discussed and compared are asymptotic approximations of the spectral integral, which are found to be accurate and computation intensive everywhere in the water and also at small depths in the bottom.