Diffraction of Kelvin waves at a sharp bend

Abstract

A closed form solution is obtained for the linearized problem of the diffraction of Kelvin waves by a sharp bend on a rotating earth. It is shown that for the frequency ω of the incoming wave less than f, where ½f is the angular velocity of rotation, the wave is transmitted around the bend without change of amplitude. For ω > f the amplitude is in general reduced but is unaltered for the special angles π/(2n + 1). For these special angles the solution is obtained in elementary terms.