Long‐range acoustic propagation in four dimensions

Abstract

Ocean acoustic modeling is usually restricted to frequency‐domain problems in two dimensions. Since ocean acoustics problems typically involve domains that are very large relative to a wavelength, computation times often become prohibitive when a third dimension (either time or the third spatial variable) is included. The adiabatic mode parabolic equation (PE), which has been applied to solve global‐scale problems in three spatial dimensions [Collins et al., J. Acoust. Soc. Am. 93, 2321 (1993)], is practical for solving four‐dimensional problems out to long range (i.e., hundreds of wavelengths or more). In the time domain, the adiabatic mode PE solution illustrates the flow of energy in the modal coefficients, which depend on range and azimuth.