Multi-Mode Surface Wave Diffraction by a Wedge

The phenomenological theory of multi-mode surface wave excitation is applied to the problem of diffraction of an incident surface wave being diffracted by the exterior of a wedge of arbitrary angle. The boundary conditions are of the form$(\partial/\partial n + ik \sin \mathscr{O}^{(1)}_+)(\partial/\partial n + ik \sin \mathscr{O}^{(2)}_+) u = 0$, i.e., multimode impedance conditions on one face of the wedge, while the wave function u vanishes on the other face. The solution extends previous work for the right-angled wedge. It is obtained by generalizing the technique devised by Maliuzhinets for treating an arbitrary wedge with a single impedance condition. In fact, it is expressed in an elementary way by functions defined by him. Qualitative features of the solution are in agreement with mathematical phenomena observed in other surface wave investigations. In particular, the leading term of the cylindrically radiating field vanishes along the surface. Simplifications also occur for certain wedge angles. Thus, despite the novel boundary conditions, the problem turns out to be tractable.