Hydrodynamics of periodic wave energy converter arrays

Abstract

We consider the hydrodynamics of wave energy converter (WEC) arrays consisting of periodically repeated single bodies or sub-arrays. Of special interest is the array gain due to wave interactions as a function of the spatial configuration of the array. For simplicity, we assume identical WECs oscillating in heave only, although the results should extend to general motions. We find that array gains can be as high as $O(10)$ compared to the same WECs operating in isolation. We show that prominent decreases in array gain are associated with Laue resonances, involving the incident and scattered wave modes, for which we obtain an explicit condition. We also show theoretically that Bragg resonances can result in large decreases in gain with as few as two rows of strong absorbers. For general WEC geometries, we develop a multiple-scattering method of wave–body interactions applicable to generally spaced periodic arrays. For arrays of truncated vertical cylinders, we perform numerical investigations confirming our theoretical predictions for Laue and Bragg resonances. For a special class of multiple-row rectangular WEC arrays, our numerical results show that motion-trapped Rayleigh–Bloch waves can exist and be excited by an incident wave, resulting in sharp, narrow-banded spikes in the array gain.