Nonlinear wave crest distribution on a vertical breakwater

The probability distribution of the nonlinear, up to the second order, crest height on a vertical wall is determined under the assumption of finite spectral bandwidth, finite water depth and long-crested waves. The distribution is derived by relying on the Quasi-Deterministic representation of the free surface elevation on the vertical wall. The theoretical results are compared against experimental data obtained by utilizing a compressive sensing algorithm for reconstructing the free surface elevation on the wall. The reconstruction is pursued by starting from recorded wave pressure time histories obtained by utilizing a sequence of pressure transducers located at various levels. The comparison demonstrates an excellent agreement between the proposed distribution and the experimental data, while, notably, the deviation of the crest height distribution from the Rayleigh one is considerable.