5.5. Scattering From Curved, Rough Surfaces

Plane wave scattering by an elastic sphere with a rough surface is an example, where the Helmholtz–Kirchhoff method, due to the assumptions inherent in the Kirchhoff approximation, is applicable only in a small area of the rough sphere. Most of the rough sphere will have sound incident under very low grazing angles and does not satisfy the conditions given in Eq. (5.52). The scattering includes shadowing, multiple scattering, and surface waves excited and propagating on the surface which are not covered by the Kirchhoff approximation. However, if the rms-roughness height h is small compared to the acoustic wavelength λ and the gradient of the roughness height (the slope) is small compared to 1, the perturbation ...

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