Bragg scattering and wave-power extraction by an array of small buoys

Abstract

Future designs of systems for power extraction from ocean waves will likely involve a periodic array of absorbing units. We report an asymptotic theory of scattering and radiation by a linear array of heaving buoys in a channel and attached to power-takeoff devices. The spacing between buoys is assumed to be comparable to the incident wavelength and sea depth but much greater than the buoy size. The effects of extraction rate on the buoy motion, transmission and reflection coefficients for a range of frequencies in and outside the band gap are studied. It is found that strong reflection for frequencies inside the band gap of Bragg resonance reduces the extraction efficiency significantly. For comparison an alternate theory for the efficiency away from the band gap is derived using Froude–Krylov approximation. The predictions confirms and complements the asymptotic theory.