Extreme waves, modulational instability and second order theory: wave flume experiments on irregular waves

Here we discuss the statistical properties of the surface elevation for long crested waves characterized by Jonswap spectra with random phases. Experiments are performed in deep water conditions in one of the largest wave tank facilities in the world. We show that for long-crested waves and for large-values of the Benjamin-Feir index, the second order theory is not adequate to describe the tails of the probability density function of wave crests and wave heights. We show that the probability of finding an extreme wave can be underestimated by more than one order of magnitude if second order theory is considered. We explain these observed deviations in terms of the modulational instability mechanism that for large BFI can take place in random wave spectra