The linearized problem of Kelvin wave diffraction at the sharp edge of a thin semi-infinite barrier on a rotating earth is considered in the case when a discontinuity in depth stems from the edge in a direction parallel to the barrier. The solution in closed form is obtained using the Wiener-Hopf technique.

It is shown that the direct effect of the depth discontinuity is always to divert additional energy away from the barrier, in the form of outgoing cylindrical waves if the period is small, and provided conditions are suitable as double Kelvin waves if the period is sufficiently long. Results suggest that Kelvin waves which are the most persistent in following an irregular coastline bounding a sea of abruptly varying depth are of intermediate period.