Oblique water-wave scattering by small undulation on a porous sea-bed

The problem of scattering of obliquely incident surface water waves by small undulation on a sea-bed is considered for solution by assuming that the bed is composed of porous material of a specific type. The reflection and transmission coefficients are determined approximately after assuming a perturbation analysis in conjunction with the Fourier transform technique, in terms of the first order of smallness of an undulation parameter $\varepsilon$ introduced in the description of the sea-bed. The special case of a patch of sinusoidal ripples on the bed is handled in detail and numerical results are presented graphically