The diffraction of surface waves by plane vertical obstacles

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Abstract
A short-wave asymptotic solution is derived for the problem of the diffraction of a surface wave train, in deep water, by a two-dimensional obstacle with plane vertical sides near its intersection with the free surface. Using matched asymptótic approximations, a detailed analysis is presented for the special case of a rectangular scatterer of depth a and width 2b, and the solution is then generalized to deal with a wider class of geometries. It is found that the transmission coefficient, at small wavelengths, has an exponentially small factor that depends on the depths of the plane sides, and an algebraically small factor that depends on the corner angles.

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