Effect of the initial spectrum on the spatial evolution of statistics of unidirectional nonlinear random waves

Results of extensive experiments on propagation of unidirectional nonlinear random waves in a large wave tank are presented. The nonlinearity of the wavefield determined by the characteristic wave amplitude and the dominant wave length was retained constant in various series of experimental runs. In each experimental series, initial spectra of different shape and/or width were considered. Every series contained sufficient number of independent realizations to ensure reliable statistics. Evolution of various statistical parameters along the tank was investigated. It is demonstrated that the spectrum width plays an important role in the evolution of the random wavefield and strongly affects the variation of the wave spectrum as well as of parameters that characterize the deviation of the wavefield statistics from that corresponding to the Gaussian distribution. In particular, in a random wavefield that initially contains independent free harmonics within a narrow spectrum, extremely steep waves appear more often in the process of evolutions than predicted by a Rayleigh distribution, while for wider initial wave spectra the probability of those waves decreases sharply and is well below the Rayleigh values.