Interaction of water surface waves with periodic and quasiperiodic cylinder arrays

Abstract

Inspired by transformation optics and photonic crystals, this paper presents a computational investigation into the interaction between water surface waves and array waveguides of cylinders with multiple previously unexplored lattice geometries, including, for the first time, quasiperiodic geometries. Extending beyond conventional square and hexagonal periodic arrays, transformation optics has opened up entirely new opportunities to investigate water wave propagation through arrays based on quasiperiodic lattices, and quasiperiodically arranged vacancy defects. Using the linear potential flow open-source code Capytaine, missing element and $\tau$-scaled Fibonacci square lattices, the Penrose lattice, hexagonal $H_{00}$ lattice and Ammann–Beenker lattice are investigated. The existence of band gaps for all arrays is observed. A hexagonal lattice with vacancy defects transmits the least energy. Bragg diffraction consistent with azimuthal rotational symmetry is observed from all arrays. Bragg resonance causes reflection from arrays, resulting in multiple Bloch band gaps. Away from Bragg resonance, waves will distort significantly to achieve periodic relationships with arrays, supporting transformation-based waveguides. The possible uses include adaptation to more versatile waveguides with applications such as offshore renewable energy and coastal defence.