The optimal design of a flap gate array in front of a straight vertical wall: resonance of the natural modes and enhancement of the exciting torque

We consider a wave energy converter made of an array of Q neighbouring floating flap gates with finite thickness in front of a straight vertical wall in constant depth. Solutions of the radiation and scattering problems are achieved by application of Green's theorem and Green's function yielding a system of hypersingular integral equations for the velocity potential expanded in terms of Legendre polynomials. We investigate how the distance between the array and the vertical wall affects the performance of the array under the action of monochromatic and random waves. We show that large values of the exciting torque on the gates can be obtained by tuning the wall distance with the resonance of the natural modes of the array; this in turn yields large power extraction for a wide range of frequencies.