Linear and Nonlinear Rogue Wave Statistics in the Presence of Random Currents

Abstract

We review recent progress in modeling the probability distribution of wave heights in the deep ocean as a function of a small number of parameters describing the local sea state. Both linear and nonlinear mechanisms of rogue wave formation are considered. First, we show that when the average wave steepness is small and nonlinear wave effects are subleading, the wave height distribution is well explained by a single "freak index" parameter, which describes the strength of (linear) wave scattering by random currents relative to the angular spread of the incoming random sea. When the average steepness is large, the wave height distribution takes a very similar functional form, but the key variables determining the probability distribution are the steepness, and the angular and frequency spread of the incoming waves. Finally, even greater probability of extreme wave formation is predicted when linear and nonlinear effects are acting together.

25 pages, 12 figures

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• Experimental Observation of a Fundamental Length Scale of Waves in Random Media
• Branched Flow
• Shaping the Branched Flow of Light through Disordered Media
• Rogue events in complex linear and nonlinear photonic media
• Machine-Guided Discovery of a Real-World Rogue Wave Model
• Rogue waves in discrete-time quantum walks
• Rogue waves in quantum lattices with correlated disorder
• Symmetric influence of forward and opposing tidal currents on rogue wave statistics
• Asymmetric integrable turbulence and rogue wave statistics for the derivative nonlinear Schrödinger equation
• The Impact of Spatial Correlation in Fluctuations of the Refractive Index on Rogue Wave Generation Probability