Kinematics Under Extreme Waves

Four different methods for prediction of wave-zone particle velocities under steep crests in random seas are compared. The study includes linear prediction, a second-order random wave model, Wheeler’s method, and a new method proposed by Grue et al. (2003). Comparison to laboratory data is also made. The purpose is to observe and evaluate differences in predictions for high and extreme waves, and how well they agree with measurements. The whole range from below still water level up to the free surface is considered. It is found that the second-order random wave model works best at all levels of the water column under a steep crest in deep water, and is therefore recommended. Grue’s method works reasonably well in many cases for z > 0, i.e. above the calm water level, but it overpredicts the velocities for z < 0. Wheeler’s method, when used with a measured or a second-order input elevation record, predicts fairly well the velocities at the free surface z = η_max, but it underpredicts around z = 0 as well as at lower levels. The relative magnitude of this underprediction is slightly lower 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 also at the free surface.