ON THE STATISTICS OF IRREGULAR SECOND-ORDER WAVES

It is well known that surface waves are skewed: due to nonlinear effects the crests are higher than the troughs are deep. Common wave models that include this asymmetry are largely limited to regular waves, while irregular (random) wave models are typically symmetric (Gaussian). Models are proposed here to account both for wave irregularity and asymmetry. Specifically, a second-order finite-depth Stokes model is formulated for random waves. Convenient methods are shown to calculate the wave skewness (normalized third-order moment of the probability distribution) for an arbitrary spectrum of first-order wave energy. Narrow-band limits that allow simple, analytic estimates of skewness and kurtosis are also derived. The theoretical predictions of the skewness in various sea states are compared with radar measurements from the Ekofisk area in the North Sea, showing very good agreement. Differences between simultaneous buoy and and a possible explanation why buoy measurements show lower skewness values is suggested. Finally, the calculated wave moments are used as input to an analytical non-Gaussian random process model, from which the extreme wave crest can be estimated. For a seastate typical of extreme North Sea conditions, the resulting extreme crest leads to lower deck-height requirements than those from a standard, deterministic Stokes fifth-order wave profile.