NON-LINEAR WIND-GENERATED WAVES FORCES ON A VERTICAL WALL

Abstract eng:
The statistical properties of some narrow-band second-order processes in the mechanics of sea waves in front of a vertical wall are investigated. Arena & Fedele (2002) have shown that the asymmetry between the crest and the trough distributions on a vertical wall is markedly greater than the asymmetry crest-trough in an undisturbed field, either for the free surface displacement or for the fluctuating wave pressure at a fixed depth. In this paper the narrow-band second-order wave force and overturning moment on the vertical wall are derived by analytical integration of the wave pressure. It is obtained that for a fixed threshold of the probability of exceedance, if kd is smaller than 1.38 (being k the wave number and d the bottom depth), positive peaks of the wave force process (that occur with the wave crests of free surface displacement on the wall) are greater than absolute value of negative peaks (that occur with the wave trough). The wave force is a quasi-symmetric process for kd=1.38: the non-linearities are weak and both the positive peak distribution and the negative peak (in absolute value) distribution are given by the Rayleigh law with good approximation. Finally it is noteworthy that for kd>1.38 we find that the wave troughs of surface displacement at wall produce negative peaks of the wave force that are (in absolute value) greater than positive peaks produced by wave crests. The predictions are in good agreement with the data of a small-scale field experiment (Boccotti, 2000).

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