Theory of the synchronous motion of an array of floating flap gates oscillating wave surge converter

We consider a finite array of floating flap gates oscillating wave surge converter (OWSC) in water of constant depth. The diffraction and radiation potentials are solved in terms of elliptical coordinates and Mathieu functions. Generated power and capture width ratio of a single gate excited by incoming waves are given in terms of the radiated wave amplitude in the far field. Similar to the case of axially symmetric absorbers, the maximum power extracted is shown to be directly proportional to the incident wave characteristics: energy flux, angle of incidence and wavelength. Accordingly, the capture width ratio is directly proportional to the wavelength, thus giving a design estimate of the maximum efficiency of the system. We then compare the array and the single gate in terms of energy production. For regular waves, we show that excitation of the out-of-phase natural modes of the array increases the power output, while in the case of random seas we show that the array and the single gate achieve the same efficiency.