Spectral collocation methods for leaky waves in submerged and buried elastic waveguides

Leaky waves constitute an important class of guided waves that propagate in waveguides adjacent to infinite fluid or solid media. A mismatch in material properties between the waveguide and its surroundings causes the radiation of energy away from the waveguide and the attenuation of the propagating wave. Such waves are encountered in a wide range of settings, from non-destructive evaluation and submerged pipes to medical ultrasound and bone surrounded by tissue. Thus, a thorough understanding of the mechanisms underlying their propagation, and particularly of their dispersion curves, is essential for many applications. Despite this, the numerical schemes traditionally employed for the computation of these dispersion curves are significantly compromised by the complex wavenumbers associated with leaky waves and their exponential growth in amplitude away from the waveguide. The work presented in this thesis proposes a spectral collocation method that overcomes those numerical challenges and aims towards a fully automated approach for the computation of leaky wave dispersion curves. To demonstrate the method, a typical situation is studied first: waves radiating from a straight elastic waveguide with a fluid on either side. The novelty of the work lies in the use of complex coordinate transformations that facilitate the numerical decay of the radiated field while also preserving all its physical characteristics; solving the leaky wave problem then becomes a matter of solving a numerically decaying one in complex space. Building on this approach, problems of increased complexity were subsequently investigated. These include the computation of leaky wave dispersion curves of waves in plates embedded in elastic media or submerged hollow cylinders, and the computation of scattered fields in closely linked underwater scattering response problems. The validity of the method was established through comparisons of predicted dispersion curves against those of commercially available software, numerical experiments with finite elements, and analytic formulations.