  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.
