Semi-analytical solution for three-dimensional underwater acoustic propagation from a directional source

This article presents a semi-analytical solution for 3D underwater acoustic propagation from a directional source within the framework of adiabatic normal modes. The solution is derived from a double-summation expression provided by the adiabatic mode model using the Fraunhofer far-field approximation and Taylor series expansions to simplify the source-strength integral for directional radiation from a complex source. The derived solution is validated through comparisons with a 2D normal mode code for a directional source in a Pekeris waveguide. Two additional examples highlight the solution’s effectiveness in complex engineering problems, including directional propagation under moving internal wave conditions and underwater radiated noise from a vessel near Long Island Sound. A key advantage of this method lies in its semi-analytical formulation, which reduces the process of incorporating source directivity into 3D underwater acoustic propagation to a single propagation model run. Even in fully 3D scenarios, when the transverse eigenfunctions of vertical modal coefficients are coupled, the Dirichlet-to-Neumann operator representing the radiation condition can be stored and reused if the directional source term changes. This improves computational efficiency and reduces numerical costs. Furthermore, the method’s full-angle propagation capability ensures an accurate description of the detailed characteristics of complex sources.