Kinematics Under Extreme Waves

Nonlinear contributions in near-surface particle velocities under extreme crests in random seas can be important in the prediction of wave loads. Four different prediction methods are compared in this paper. The purpose is to observe and evaluate differences in predicted particle velocities under high and extreme crests, and how well they agree with measurements. The study includes linear prediction, a second-order random wave model, Wheeler’s method [1970, “Method for Calculating Forces Produced by Irregular Waves,” JPT, J. Pet. Technol., pp. 359–367] and a new method proposed by Grue et al. [2003, “Kinematics of Extreme Waves in Deep Water,” Appl. Ocean Res., 25, pp. 355–366]. Comparison to laboratory data is also made. The whole wave-zone range from below still water level up to the free surface is considered. Large nonlinear contributions are identified in the near-surface velocities. The results are interpreted to be correlated with the local steepness $kA$⁠. Some scatter between the different methods is observed in the results. The comparison to experiments shows that among the methods included, the second-order random wave model works best in the whole range under a steep crest in deep or almost deep water, and is therefore recommended. The method of Grue et al. works reasonably well for $z>0$⁠, i.e., above the calm water level, while it overpredicts the velocities for $z<0$⁠. Wheeler’s method, when used with a measured or a second-order input elevation record, predicts velocities fairly well at the free surface $z=ηmax$⁠, but it underpredicts around $z=0$ and further below. The relative magnitude of this latter error is slightly smaller than the local steepness $kA0$ and can be quite significant in extreme waves. If Wheeler’s method is used with a linear input, the same error occurs in the whole range, i.e., also at the free surface.