Rogue Waves and Large Deviations in Deep Sea

G. Dematteis, T. Grafke, and E. Vanden-Eijnden, Proc. Natl. Acad. Sci., 115 (2018), 855-860


The appearance of rogue waves in deep sea is investigated using the modified nonlinear Schrödinger (MNLS) equation with random initial conditions that are assumed to be Gaussian distributed, with a spectrum approximating the JONSWAP spectrum obtained from observations of the North Sea. It is shown that by supplementing the incomplete information contained in the JONSWAP spectrum with the MNLS dynamics one can reliably estimate the probability distribution of the sea surface elevation far in the tail at later times. Our results indicate that rogue waves occur when the system hit small pockets of wave configurations hidden in the core of their distribution that trigger large disturbances of the surface height via modulational instability. The rogue wave precursors in these pockets are wave patterns of regular height but with a very specific shape that is identified explicitly, thereby allowing for early detection. The method proposed here builds on tools from large deviation theory that reduce the calculation of the most likely rogue wave precursors to an optimization problem that can be solved efficiently.