The Effect of Third Order Nonlinearities on the Statistical Distributions of Wave Heights, Crests and Troughs in Bimodal Crossing Seas

Abstract

This paper investigates the effect of thirdorder nonlinearities on the statistical distributions of wave heights, crests, and troughs of waves mechanically generated in a deepwater basin and simulating two crossing systems characterized by bimodal spectra. The observed statistics exhibits various effects of thirdorder nonlinearities, in a manner dependent on both the distance from the wavemaker and the angle between the mean directions of the component wave systems. In order to isolate and demonstrate the effects of thirdorder nonlinearities by themselves, the vertically asymmetric distortions induced by secondorder bound waves are removed from the observed time series. It appears then that the distributions of wave crests, troughs and heights extracted from the nonskewed records clearly deviate from the Rayleigh distribution, suggesting that the waves are characterized by nonlinear corrections of higherorder than the typical of secondorder waves. Nonetheless, some models developed for weakly nonlinear secondorder waves can still be used in describing wave heights, crests and troughs in mixed seas, provided that the relevant distribution parameters are modified, so as to reflect the effects of thirdorder corrections and some basic characteristics of the mixed seas.