Chaotic and fractal properties of laboratory-generated surface water waves

Summary

We report the results of four laboratory experiments on surface water waves generated with the Pierson-Moskowitz power spectrum, and characterized by different values of the ratiof _p/f _N and of the water depthh. The scope of the experiments was to test the dependence of the chaotic and fractal properties of the data on the parameterf _p/f _N, which has been indicated as determinant by previous numerical studies; the different water depths are used to induce different levels of non-linearity in the records. The analysis indicates that the Grassberger and Procaccia correlation integrals, the largest Lyapunov exponent and the scaling exponent of the data sets considered herein are completely assimilable to those of numerically generated linear time series; the algorithms used are insensitive to the presence of non-linearities because they sample essentially the high-frequency components.