A semi-linear method for particle kinematics under steep randomwave crests

The determination of random wave kinematics in high sea-states especially in the region above mean water surface has been a major challenge and most proposed methods are not robust. In this work, a method which is similar to stretching and extrapolation in its simplicity is developed based on a simplified form of wave-wave interaction which is robust to 2^nd order. To check the usefulness of the new method, horizontal particle velocity results are compared with Zhang's HWM, Wheeler stretching, linear extrapolation above MWL, experimental measurements and theoretical computations of Longridge et al (1996), Skjelbriea et al (1991) and Stansberg et al (2006). Results of the new method show good agreement with the results of Skjelbriea et al (1991) and are closer to experiment than 2^nd order results of Stansberg et al (2006) while only showing a qualitative agreement with Longridge et al (1996). The poorer comparison with Longridge et al (1996) is probably because it was not possible to reproduce the exact time series used by Longridge et al as the exact amplitudes and phases were not available. The improved capability of the new method over existing methods has thus been demonstrated and its advantage over the HWM lies in being simpler to implement.