Rogue waves and large deviations in deep sea

Abstract

The appearance of rogue waves in deep sea is investigated by using the modified nonlinear Schrödinger (MNLS) equation in one spatial dimension with random initial conditions that are assumed to be normally distributed, with a spectrum approximating realistic conditions of a unidirectional sea state. 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. Our results indicate that rogue waves occur when the system hits unlikely pockets of wave configurations that trigger large disturbances of the surface height. 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 combines Monte Carlo sampling with tools from large deviations theory that reduce the calculation of the most likely rogue wave precursors to an optimization problem that can be solved efficiently. This approach is transferable to other problems in which the system's governing equations contain random initial conditions and/or parameters.

Practical rare event sampling for extreme mesoscale weather

“…A burgeoning field of research explicitly links rare event simulation and analysis tools with geophysical applications [9][10][11][12][13][14] . In a recent paper, Ragone, Wouters and Bouchet 12 showed that rare event sampling methods can be used to study the probability of extreme weather occurring.…”

Sequential sampling strategy for extreme event statistics in nonlinear dynamical systems

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A variational approach to probing extreme events in turbulent dynamical systems

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