The influence of spectral cutoff in random wave simulations

When investigating large ocean waves we frequently run simulations or experiments with random waves. For practical reasons such seastates are often initalised without the full spectral tail which would normally be present in the ocean. The change in the distribution of energy associated with this is generally very small and it impact on subsequent wave statistics presumed negligible. Here we investigate this by running firstly fully non-linear simulations of the sea-state considered in the experiments of Latheef & Swan (2013) and secondly Modified non-linear Schrödinger equation simulations of the experiments of Onorato et al. (2009). We find a consistent pattern across our simulations (which are also consistent with other results in the literature). We find that the curtailing of the spectrum in the initial conditions has a significant impact on the subsequent wave statistics—cutting off the spectrum leads to significantly more rogue waves than would otherwise be expected. We attribute this to the curtailed spectrum being far from equilibrium and this driving a strongly non-linear response. The results presented here are only for directionally spread waves—unidirectional waves are not expected to show the same physics.