On Adiabatic Normal Modes in a Wedge-Shaped Sea

Abstract

A two-dimensional problem that is a model for sound propagation in a narrow water wedge near the shore of a sea is studied. A solution to the Helmholtz equation, which is asymptotically a normal wave propagating along “water” wedge to the “shore,” is constructed explicitly. The solution satisfies the Helmholtz equation in the quadrant one side of which is “the surface of the water” and the second is perpendicular to it, starts at the top of the wedge and goes into the “bottom.” Boundary conditions on wedge boundaries and at infinity in the “bottom” are satisfied.