Numerical investigation on local resonance within an array of C-shaped cylinders in water waves

In this work, computational fluid dynamics (CFD)—based simulations and linear diffraction analysis are carried out to investigate the interaction between water waves and metamaterials composed of an array of C-shaped cylinders. The flow visualization by CFD-based simulations reveals that local resonance is a result of constructive interference between the incident wave and the wave radiated from the cavity of the C-shaped cylinder. The wave-induced water motion inside the cavity acts as a source of generating this radiated wave, which has the same angular wave frequency and wavenumber but opposite propagation direction as the incident wave. In addition, it is found from the CFD-based simulations that the energy dissipation increases as the opening of the C-shaped cylinder becomes shorter and sharper, along with an increase in its outer radius, and the variation trend of energy dissipation is only affected by the outer radius. Meanwhile, except for very small opening lengths, variations in opening length, width, and outer radius do not significantly impact the wave attenuation effect of the C-shaped cylinder array. Moreover, the results obtained by CFD and the linear potential flow model are compared. The linear potential flow theory is proven to be a reliable approach for accurately predicting the local resonant frequency and transmission coefficients within the local resonant band across a range of geometric parameters. However, it is noted that this theory may have limitations when applied to cases with extremely small opening lengths, where it struggles to accurately predict the local resonant frequency and the intensity of local resonance.