Non-Gaussian Wave Groups Generated in an Offshore Wave Basin

Abstract

The main goal of the present paper is to study the differences of the descriptors of the wave groups in the nonlinear case in comparison with the same parameters for a Gaussian process. The data analyzed are from a deep water basin of Marintek. They consist of sequence of five identical independent experimental runs of unidirectional waves measured at ten fixed points situated in different distances from the wave maker. Each series contain about 1800 waves. Thus the statistics collected from a given gauge comprise about 9000 waves combined in a number of wave groups. Because the series describe a process significantly different from the Gaussian one, an upper and lower envelopes are introduced as lines which connect the peaks of the crests and the lower points of the troughs respectively. Spline functions are applied to calculate these envelopes. Then, the mean high run and mean group length are estimated for different levels, their ensemble average over five experimental runs is found for every gauge and is compared with the results of the theory of Gaussian process. It is found that the values of the mean time intervals of the groups correlate with coefficient of kurtosis of the process. It is determined also that mean group length is shorter and the mean high run is larger for the nonlinear wave groups in comparison with the Gaussian wave groups. The modification of wave groups in space and time is investigated in the work as well. Wigner time-frequency spectrum with Choi-Williams kernel is applied to describe the process of entire modulation and demodulation of the groups. It is found that before formation of the high wave a wave down-shifting takes place. At this stage the local spectrum is relatively narrow and the group shrinks continuously. Close to the focus the time-frequency spectrum is very wide and the group has a triangle form. Further the high wave breaks and the wave group acquires the form of “three sisters.” The transform of the group continues by its disintegration, the local spectrum stands narrow and an up-shifting is observed.