Bragg scattering of surface waves by periodic bars: theory and experiment

Abstract

We extend a recent linearized theory on Bragg scattering of surface waves by periodic sandbars to include second-order effects of the free surface and of the bars. New experiments are performed to verify the existence of the cutoff detuning frequency, the dispersive nature of the first-order wave envelope, and the radiation of second-order long waves. Measured transient and quasi-steady responses to incident wave packets and uniform wavetrains are compared with corresponding theoretical results. For quasi-steady incident waves of relatively small steepness it is found necessary to improve the theory to the second order in bar slope, in order that the calculated short-wave envelopes agree with those measured over the bars.