### ASA 124th Meeting New Orleans 1992 October

## 5pPA3. A T matrix for scattering from a doubly infinite fluid--solid
interface with doubly periodic surface roughness.

**Judy Smith
**

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Garner C. Bishop
**

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*Naval Undersea Warfare Ctr. Div., Newport, RI 02841-5047
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The T-matrix formalism is used to calculate scattering of a pressure 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 field, the surface fields, and
scattered pressure field in the fluid and displacement field in the solid, are
represented by infinite series of 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
spectral amplitudes of the scattered fields is constructed. An exact analytic
solution and numerical results are obtained for scattering from a doubly
periodic rough surface constructed by superposing two sinusoids each of which
depends on a single but different orthogonal coordinate.