Second-Order Kinematics Underneath Irregular Waves

The present paper is concerned with the prediction of horizontal velocities underneath measured irregular wave surface elevations. The simple case of unidirectional waves in deep water is considered. The main challenge in calculating accurately the kinematics in the crest region is related to the treatment of the contribution from wave components with frequencies much higher than the frequencies near the spectral peak. When using linear or weakly nonlinear perturbation methods, the wave components are superimposed at the still water level and it is necessary to truncate the tail of the spectrum in order to calculate accurately the velocity in the crest region.In the present paper, results from three methods of calculating the crest kinematics are compared with the model test results of Skjelbreia et al. [1]:• The second-order model of Stansberg et al. [5] which truncates consistently the high frequency part of the spectrum.• The second-order model of Johannessen [13] which calculates the velocity directly at the instantaneous free surface.• The Wheeler [3] stretching method which stretches the linear velocity profile from the still water level to the instantaneous free surface.In addition to comparing the horizontal velocity profiles underneath the crest, time traces of horizontal velocity is compared at the free surface in the vicinity of a large crest. The latter comparison highlights the differences between the models and the challenge of accurate predictions close to top of crest. All three models show a reasonable agreement with model test results although it is clear that the first two methods are superior to the Wheeler method.© 2013 ASME