Surface wave interactions with systems of oscillating bodies and pressure distributions

Abstract

Theoretical descriptions of arrays of wave-power devices have been given previously for systems consisting of either oscillating bodies or oscillating pressure distributions. A number of devices have an oscillating water column placed within a floating structure, thus there is a need for a general theory describing composite systems of both oscillating bodies and pressure distributions. Such a theory is presented here. The states of the oscillators in the system are described by the complex amplitudes of the air-pressure distributions within floating or submerged chambers, and of the velocity components for oscillating bodies. By analogy with electric circuit theory, the radiation coupling between all oscillators is represented by a partitioned matrix composed of the radiation admittance matrix for the pressure distributions, the radiation impedance matrix for the oscillating bodies, and a radiation coupling matrix between the bodies and the pressure distributions. Using potential theory of an ideal fluid some reciprocity relations involving these matrices are derived. A little-known relationship between the added mass matrix and the energy of the near-field motion due to oscillating bodies is generalised to include pressure distributions. Previously, only the proof of the result for a single oscillating body has been published. By joining eigenfunction expansions on the common boundaries of rectangular domains, numerical results are obtained for a two-dimensional system where a pressure distribution is trapped between two rigidly connected vertical barriers which are able to oscillate in the surge mode. It is shown that this system absorbs all of the incident wave power, provided optimum values of the complex oscillation amplitudes can be achieved.