A T matrix for scattering from a doubly infinite fluid–solid interface with doubly periodic surface roughness

The T‐matrix formalism is used to calculate scattering of a plane wave from a doubly infinite fluid–solid interface with doubly periodic surface roughness. The Helmholtz–Kirchhoff integral equations are used to represent the scattered pressure field in the fluid and the displacement field in the solid. The boundary conditions are applied and a system of four coupled integral equations is obtained. The incident and scattered pressure fields in the fluid, as well as the surface pressure field, are represented by infinite series of scalar Floquet plane waves, while the scattered displacement field in the solid and the surface displacement field are represented by infinite series of rectangular vector basis functions constructed from Floquet plane waves. This process discretizes the integral equations and transforms them into a system of four coupled doubly infinite linear equations. The extended boundary condition is applied and the T matrix that relates the spectral amplitudes of the incident field to the s...