Nonlinear wave transformations and randomness

Variations of raw spectral estimates of ocean waves with quite different sea states are examined for confirming their fitness to theoretical chi-square distribution with two degrees of freedom. A hypothetical numerical experiment is devised and histograms of spectral variability for artificially produced initial wave spectrum of constant shape undergoing nonlinear transformations are computed and compared with the chi-square distribution. As the nonlinear energy transfer among wave components develops, the histograms of spectral variability, initially constant, evolve to the exponentially decaying chi-square form. Once the variability distribution attains the exponential form it remains so regardless of the change in wave field characteristics, as for waves becoming linear by propagating into deeper regions. Irreversible nonlinear wave transformations not only redistribute the spectral energy broadly but also do it by imparting a variability to spectral components which accords with the chi-square distribution, indicating true randomness.