Experimental Evidence of Hydrodynamic Instantons: The Universal Route to Rogue Waves

Abstract

A statistical theory of rogue waves is proposed and tested against experimental data collected in a long water tank where random waves with different degrees of nonlinearity are mechanically generated and free to propagate along the flume. Strong evidence is given that the rogue waves observed in the tank are hydrodynamic instantons, that is, saddle point configurations of the action associated with the stochastic model of the wave system. As shown here, these hydrodynamic instantons are complex spatio-temporal wave field configurations, which can be defined using the mathematical framework of Large Deviation Theory and calculated via tailored numerical methods. These results indicate that the instantons describe equally well rogue waves that originate from a simple linear superposition mechanism (in weakly nonlinear conditions) or from a nonlinear focusing one (in strongly nonlinear conditions), paving the way for the development of a unified explanation to rogue wave formation.

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• Extreme event probability estimation using PDE-constrained optimization and large deviation theory, with application to tsunamis
• Statistics of extreme events in integrable turbulence
• Rare event-triggered transitions in aerodynamic bifurcation
• Instantons and the path to intermittency in turbulent flows
• Engineering Optical Rogue Waves and Breathers in a Coupled Nonlinear Schrödinger System with Four-Wave Mixing Effect
• Numerical spectral synthesis of breather gas for the focusing nonlinear Schrödinger equation
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• Anomalous Statistics and Large Deviations of Turbulent Water Waves past a Step
• Rogue ocean waves and the St. Petersburg paradox
• Instantons, fluctuations and singularities in the supercritical stochastic nonlinear Schroedinger equation
• Forced symmetry breaking as a mechanism for rogue bursts in a dissipative nonlinear dynamical lattice