1 Introduction

An important factor in designing offshore structures is the determination of its deck elevation. Generally, the requirement will be that an extreme wave crest shall not hit the deck. This extreme wave crest may be estimated in various ways. Real surface waves are both irregular and skewed: due to nonlinear effects the crests are higher than the troughs are deep. Typical deterministic approaches account for skewness but not irregularity. For example, the extreme crest height is commonly estimated from a deterministic (regular) Stokes wave profile, with wave height and period related to the significant wave height and period of an extreme seastate. To include both wave irregularity and skewness, we follow a different approach in the present study. A Stokes" expansion of finite water depth random sea is carried out to second order and the skewness parameter (normalized third-order moment of the probability distribution) is calculated. The skewness is used as input to a Hermite polynomial transformation model, Winterstein (1988), from which the extreme value of the nonlinear and hence non-Gaussian wave crests can be estimated analytically. The theoretical predictions of the skewness in various sea states are compared with field measurements from the Ekofisk area in the North Sea, showing very good agreement. Differences between simultaneous buoy and radar measurements are discussed, and a different secondorder elevation is derived for comparing the theory with buoy measurements, accounting for the fact that the buoy estimates the surface elevation based on measured accelerations. The skewness of irregular second-order waves was studied theoretically by Longuet-Higgins (1963) in the case of infinite water depth. Irregular second-order waves include waves that have wavenumbers equal to the sums and the differences of those of the first-order waves.

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