Non-Gaussian Statistics of Mechanically Generated Unidirectional Irregular Waves

Abstract

An experimental study is presented on the non-Gaussian statistics of random unidirectional laboratory wave fields described by JONSWAP spectra. Relationships between statistical parameters indicative of the occurrence of large-amplitude waves are discussed in the context of the initial steepness of the waves combined with the effect of spectral peakedness. The spatial evolution of the relevant statistical and spectral parameters and features is also considered. It is demonstrated that over the distance the spectra exhibit features typical for developing nonlinear instabilities, such as spectral broadening and downshift of the peak, along with lowering of the high-frequency tail and decrease of the peak magnitude. The wave fields clearly show an increase of third-order nonlinearity with the distance, which can be significant, depending on the input wave environment. The steeper initial conditions, however, while favouring the occurrence of extremely large waves, also increase the chances of wave breaking and loss of energy due to dissipation, which results in lower extreme crests and wave heights. The applied Miche-Stokes-type criteria do confirm that some of the wave extremes exceed the limiting individual steepness. Eventually, this result agrees with the observation that the largest number of abnormal waves is recorded in sea states with moderate steepness.