Weakly nonlinear theory for a gate-type curved array in waves

Abstract

We analyse the effect of gate surface curvature on the nonlinear behaviour of an array of gates in a semi-infinite channel. Using a perturbation-harmonic expansion, we show the occurrence of new detuning and damping terms in the Ginzburg–Landau evolution equation, which are not present in the case of flat gates. Unlike the case of linearised theories, synchronous excitation of trapped modes is now possible because of interactions between the wave field and the curved boundaries at higher orders. Finally, we apply the theory to the case of surging wave energy converters (WECs) with curved geometry and show that the effects of nonlinear synchronous resonance are substantial for design purposes. Conversely, in the case of subharmonic resonance we show that the effects of surface curvature are not always beneficial as previously thought.

Hydrodynamics of large wave energy converter arrays with random configuration variations

“…In such cases, the linear assumption is no longer valid, and a nonlinear interaction theory should be employed. Studies on weakly nonlinear interactions in arrays of surge-type devices (Michele, Renzi & Sammarco 2019; Michele & Renzi 2019) show that nonlinear resonance effects can be substantial. With the increase of randomness, however, the resonance effects and the associated large amplitudes are significantly diminished, so the linear theory should be even more generally valid.…”

Niche Applications and Flexible Devices for Wave Energy Conversion: A Review

“…Michele et al [35] have recently proposed a system of multiple curved gates in a harbour channel, as shown in the conceptual scheme of Figure 6. Unlike isolated floating bodies, a system of closely spaced gates achieves optimal efficiency when they resonate as a whole.…”

“…Michele et al [35,37] developed second and third order theories for arrays of surging gates in a channel and of flapping plates in open sea. They showed that hydrodynamic interactions between weakly nonlinear waves and floating bodies characterised by curved surfaces yield large efficiency (C F ∼ 0.7 in optimal configuration at synchronous resonance).…”

Wave Energy Extraction by Flexible Floaters

“…Note also that the maxima are located in correspondence to the first eigenfrequencies of the system, i.e., ω i = 0.99, 1.55, 2.24, 2.77, 3.66, 5.06 Rad s −1 . As in the case of oscillating wave surge converters and oscillating water columns [17,18,[20][21][22][23][24], resonance of natural modes is beneficial in terms of power extraction efficiency.…”