Nonlinear Properties of Laboratory Wind Waves at Energy Containing Frequencies

Part 1. Probability Density Distribution of Surface Elevation

Abstract

Nonlinear properties of wind waves in a wind-wave tunnel are investigated bymeasuring the probability density distribution of surface elevation. The surface elevationdistribution of raw records are found to have a positive skewness (K₃=0.21 to 0.43) and anegative kurtosis (K₄=-0.74 to -0.41) with magnitude depending of fetch and wind speed.The values of skewness are in qualitative agreement with a prediction of the weak interactiontheory for a random wave field incorporating the effects of second harmonics (Tayfun, 1980), but the values of kurtosis are different in sign from the prediction.
To examine the nonlinear properties of energy containing components, higher harmoniccomponents are excluded from the wave records by using a kind of a band-pass filter. Thesurface elevation distributions of the filtered waves show a sharp decrease in skewness (K₃'=0), but the distributions remain highly non-Gaussian with a large negative kurtosisalmost independent of the fetch and wind speed (K₄'=-0.66). It is concluded that thenegative kurtosis is due to the non-random character of the phase and amplitude among theenergy containing components, and that nonlinear interactions occur amongst the energycontaining frequencies.