Evolution of Directional Wave Spectra Through Finite Regular and Randomly Perturbed Arrays of Scatterers

A method is proposed to solve the full linear problem of wave scattering by a large finite array of circular inclusions in two spatial dimensions and compute the concomitant evolution of directional wave properties through the array. The method decomposes the array into slabs. Interactions between adjacent slabs are calculated using a representation of the wave fields scattered by each slab as integrals of plane waves over the directional spectrum plus exponentially decaying branches. The method is applied to the canonical problem of acoustic sound-hard scatterers. Validation is sought for (i) regular arrays via comparison with solutions of corresponding infinite, periodic single- and multiple row arrays and (ii) random arrays via comparison with Foldy's approximation for the effective field. A numerical investigation is conducted to determine the effect of introducing random perturbations into regular arrays on the directional properties of the reflected and transmitted fields.