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

## TL;DR

This paper presents experimental evidence that rogue waves in water tanks are hydrodynamic instantons, providing a unified statistical framework for understanding their formation through Large Deviation Theory.

## Contribution

It introduces a statistical theory identifying rogue waves as hydrodynamic instantons, validated by experiments and applicable across linear and nonlinear wave conditions.

## Key findings

- Rogue waves are identified as hydrodynamic instantons.
- Experimental data supports the instanton model.
- Unified explanation for rogue wave formation is proposed.

## 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.