Scattering by small defects at a fluid/solid interface

The scattering of incident plane elastic waves by a variety of different defects that lie upon a fluid/solid interface is considered here using matched asymptotic expansions. The expansion scheme is developed in terms of a parameter $\epsilon$, the ratio of a typical defect length scale to a typical wavelength of the incident field, taken to be small. It is shown in this specific limit that the fluid and solid problems uncouple in a particularly convenient manner allowing analytical solutions to be deduced. Three different canonical situations occur and these are illustrated via three specific examples treated here: a rigid strut, an edge crack, and a rigid strip. In each case the leading order matching is performed to identify the leading order contribution of the defect to the acoustic field in the far field. In particular, each defect is identified with a source or dipole response in interfacial stress or displacement.

Co-authored with D. P. Williams.