Large Deviations for Rogue Waves

In this project, Rogue Waves in deep sea are investigated using the modified nonlinear Schrödinger (MNLS) equation in one spatial-dimension with random initial conditions. The initial conditions approximate realistic conditions of a uni-directional sea state, taken as the JONSWAP spectrum. It is shown that one can use the incomplete information contained in this spectrum as prior and supplement this information with the MNLS dynamics to reliably estimate the probability distribution of the sea surface elevation far in the tail at later times. The Rogue Wave events encountered in numerical simulations, as well as in experiments in a 270m wave channel in Norway, agree with their most likely (instanton) configuration obtained from the theory.

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