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 spatiotemporal 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 created by simple linear superposition (in weakly nonlinear conditions) or by nonlinear focusing (in strongly nonlinear conditions), paving the way for the development of a unified explanation to rogue wave formation.
 Publication:

Physical Review X
 Pub Date:
 October 2019
 DOI:
 10.1103/PhysRevX.9.041057
 arXiv:
 arXiv:1907.01320
 Bibcode:
 2019PhRvX...9d1057D
 Keywords:

 Physics  Fluid Dynamics;
 Nonlinear Sciences  Pattern Formation and Solitons;
 Physics  Atmospheric and Oceanic Physics
 EPrint:
 Phys. Rev. X 9, 041057 (2019)