Asymptotic modelling of thermoviscous dissipation in resonant acoustic structures

In this thesis, we employ asymptotic methods to systematically develop models for studying wave propagation and absorption in resonant acoustic structures. A novel aspect of our work is the inclusion from first principles of thermoviscous effects in multiple-scale media entailing complex geometric features. We initially focus on extraordinary transmission through narrow slits and slender holes embedded in rigid slabs, using scaling arguments and the method of matched asymptotic expansions to derive accurate approximations for field enhancements within the slits and holes, deviations of resonances from the standing-wave (Fabry-Pérot) frequencies expected in the absence of aperture effects, and sound absorption. Furthermore, we find that a well-known analogy between acoustic and electromagnetic extraordinary transmission can surprisingly be extended to include dissipative effects, in the case where these are associated with thin thermoviscous and electromagnetic-skin boundary layers, respectively in the acoustic and electromagnetic scenarios. Towards generalising the theory, we reformulate our asymptotic model for a hole resonator in terms of its spectral response, and extend to the case of multiple hole resonators via a multiple-scattering (Foldy-type) scheme. Armed with that extended theory, and a homogenisation approximation of it, we illuminate the acoustic properties of finite and infinite metasurface slabs formed of doubly periodic arrays of holes, covering extraordinary transmission, coherent perfect absorption (multi-channel critical coupling), lattice resonances of finite surfaces, and surface-wave effects.