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Reflection of gravity waves by a steep beach with a porous bed

Solutions are determined for normally incident non-breaking linear gravity waves in a perfect fluid over a porous plane bed of arbitrary slope α both with and without bed friction. For simplicity, computations are restricted to α=π/2m, m∈N. Modifications to wave height transformations due to percolation and to friction are determined for a variety of slopes and coefficients. The effect on the reflection coefficient Rf is also studied and excellent qualitative agreement is found with recent work on damping and reflection by permeable structures. In particular, for a choice of parameters, the Rf response is determined in closed form.