Flap gate farm: From Venice lagoon defense to resonating wave energy production. Part 1: Natural modes

• Wave energy converter (WEC) of a flap gate type: the "gate farm" WEC, a device made of arrays of neighboring non-sparse flap gates, strongly hydrodynamically coupled.
• Rigorous novel analytical theory of the natural modes is given.
• Indication is given on how to design “correctly” a flap gate WEC in order to really enhance wave power extraction.
• Resonance of natural modes as an energy resource rather a bias like in Venice flood gates.

We consider a flap-gate farm, i.e. a series of P arrays, each made by Q neighboring flap gates, in an infinitely long channel. We show that there are P × (Q − 1) natural modes and determine their eigenfrequencies and modal forms. When the distance between the arrays goes to infinity the eigenfrequencies converge to the Q − 1 values given by Li and Mei [ 14]. For an ad-hoc combination of channel geometry and flap gate characteristics, modal excitation can give significantly larger response than for the case of a single or a sparse gate system. This aspect is relevant for the design of an optimal gate farm wave energy converter.