Modulation instabilities and non-gaussian statistics in experimental random water-wave trains

We study random, long-crested surface gravity waves in the laboratory environment. Starting with wave spectra characterized by random phases we consider the development of the modulational instability and the consequent formation of large amplitude waves. We address both dynamical and statistical interpretations of the experimental data. While it is well known that the Stokes wave nonlinearity leads to non-Gaussian statistics, we also find that the presence of the modulational instability is responsible for the departure from a Gaussian behavior, indicating that, for particular parameters in the wave spectrum, coherent unstable modes are quite prevalent, leading to the occurrence of what might be called a "rogue sea." Statistical results are also compared with ensemble numerical simulations of the Dysthe equation.