A perturbation theory, for waves on a perfect fluid in a wedge-shaped domain, is used to derive integral expressions for set-down valid up to the breaker line for arbitrary wedge angles α. Computations are carried out for a set α = π/2N, (N = 2,3,…,7,15) using a generalized Simpson quadrature and these confirm that existing theory underestimates the set-down by a factor which increases with the wedge angle. Curve fitting techniques are used to deduce a modification of the formula given by Longuet-Higgins and Stewart (1963) which can be universally implemented to estimate set-down just seaward of the breaker line. It is also noted that farther seaward the mean free surface begins to oscillate spatially, and the possible ramifications of this are discussed.
Ehrenmark, Ulf T.. 1994. "Set-down computations over an arbitrarily inclined plane bed." Journal of Marine Research 52, (6). https://elischolar.library.yale.edu/journal_of_marine_research/2120