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

TL;DR

The paper demonstrates that rogue waves can be predicted in advance using linear approximations of wave dynamics at small Benjamin-Feir indices, with reliable forecasts spanning hundreds of wave periods.

Contribution

It shows that linear dynamics can reliably predict the formation of rogue waves in nonlinear sea wave models at small Benjamin-Feir indices.

Findings

Linear approximation indicates impending rogue waves.

Forecasting window extends to hundreds of wave periods.

Prediction accuracy supports practical early warning systems.

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.