title: An explicit analytical solution for sound propagation in a three-dimensional penetrable wedge with small apex angle.
abstract: A problem of sound propagation in a shallow-water waveguide with a weakly sloping penetrable bottom is considered. The adiabatic mode parabolic equations are used to approximate the solution of the three-dimensional (3D) Helmholtz equation by modal decomposition of the acoustic pressure field. The mode amplitudes satisfy parabolic equations that admit analytical solutions in the special case of the 3D wedge. Using the analytical formula for modal amplitudes, an explicit and remarkably simple expression for the acoustic pressure in the wedge is obtained. The proposed solution is validated by the comparison with a solution of the 3D penetrable wedge problem obtained using a fully 3D parabolic equation that includes a leading-order cross term correction.
authors.affiliation: V.I.Il'ichev Pacific Oceanological Institute, 43, Baltiyskaya Street, Vladivostok, 690041, Russia.
authors.forename: Pavel S
authors.initials: PS
authors.lastname: Petrov
authors.affiliation: Laboratoire de Mécanique des Fluides et d'Acoustique, Unité Mixte de Recherche, Centre National de la Recherche Scientifique 5509, Université de Lyon, École Centrale de Lyon, 36 Avenue Guy de Collongue, F-69134 Ecully Cedex, France.
authors.forename: Frédéric
authors.initials: F
authors.lastname: Sturm