Interaction of water surface waves with periodic and quasiperiodic cylinder arrays

TL;DR

This study computationally explores how water surface waves interact with various periodic and quasiperiodic cylinder arrays, revealing band gaps and resonance effects that could inform advanced waveguide designs for offshore and coastal applications.

Contribution

It introduces the first investigation of water wave interaction with quasiperiodic and vacancy-defect arrays, expanding the understanding beyond traditional periodic structures.

Findings

All arrays exhibit band gaps.

Hexagonal array with vacancy defects transmits least energy.

Bragg diffraction observed across all 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 Amman-Beenker lattice are investigated. The existence of band gaps for all arrays is observed. An hexagonal lattice with vacancy defects transmits the least energy. Bragg diffraction consistent with rotational symmetry is observed from all arrays. Waves will distort significantly to achieve resonance 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.