Influence of the Third Order Nonlinearity on the Distribution of Wave Height Maxima in an Offshore Basin

The effect of the coefficient of kurtosis, λ₄₀, on the distribution of wave height maxima has been investigated. The data set used consists of water surface displacements in irregular deep water unidirectional wave fields generated in an offshore basin and defined by the JONSWAP spectrum. The full-scale records are of almost 3h17min duration. The measurements have been performed at ten equidistant gauges along the basin, which permits to follow the changes in wave statistics away from the wave-generator. Subsequently, the records have been split into series of different length, corresponding to N = 100, 200 and 300 waves, and the probability density functions and the exceedance probabilities of the maximum wave heights have been constructed conditional on λ₄₀. They have been compared with the modified Edgeworth-Rayleigh model of Mori and Janssen [1] applied to the maximum wave heights. The theoretical expressions are formulated as a simple function of the coefficient of kurtosis and the number of waves in the sample. The coefficient of kurtosis, reflecting the third order nonlinearity, is found to increase with the distance from the wave-maker. The considered theoretical density curves describe only qualitatively the shift of the empirical mode towards higher values. The tendency of the peak of the distribution to diminish with increase of λ₄₀ has been observed. However, the most probable wave height remains underestimated by the theory for all classes of λ₄₀, regardless of the length of the time series. Finally, the probability that a certain normalized height level H_max/H_s will be exceeded increases with the increase of λ₄₀, as being theoretically predicted, although it is overestimated by the theory in the lower range of values of λ₄₀ and underestimated over the higher range of values of λ₄₀.