A Coupled–mode Formulation for the Solution of the Helmholtz Equation in Water in the Presence of a Conical Sea-Mount

The problem of determining the acoustic field in the sea due to a point harmonic source around a penetrable sea-mount of conical shape is handled in terms of normal-mode theory. The sea-mount is divided in cylindrical segments-rings, in each of which, a series expansion of the acoustic pressure in terms of normal modes and cosine functions is considered. A similar series expansion is considered for the external field and the coefficients of the various expansions are calculated by solving linear systems of equations resulting from the application of the continuity conditions of the pressure field and normal component of the particle velocity at the artificial interfaces of the cylindrical segments-rings. Since Hankel functions of high order are involved in the expansions, numerical problems arise in the numerical implementation of the scheme in cases of low convergence rate. Numerical results are presented for some simple cases of very low frequency propagation around a cylindrical mount.