Predictability of the Appearance of Anomalous Waves at Sufficiently Small Benjamin-Feir Indices

Abstract

The numerical simulation of the nonlinear dynamics of random sea waves at moderately small Benjamin-Feir indices and its comparison with the linear dynamics (at the coincidence of spatial Fourier harmonics near a spectral peak at a certain time $t_p$) indicate that the appearance of a rogue wave can be predicted in advance. If the linear approximation shows the presence of a sufficiently extensive and/or high group of waves in the near future after $t_p$, an anomalous wave is almost necessarily formed in the nonlinear model. The interval of reliable forecasting covers several hundred wave periods, which can be quite sufficient in practice for, e.g., avoiding the meeting of a ship with a giant wave.