# Forced three-wave interactions of capillary-gravity surface waves

## TL;DR

This paper experimentally investigates forced three-wave interactions of capillary-gravity waves, revealing how viscous dissipation influences wave coupling and leads to daughter waves that do not follow the linear dispersion relation.

## Contribution

It demonstrates experimentally that viscous dissipation causes a forced three-wave interaction mechanism, expanding the understanding of wave coupling beyond traditional resonant conditions.

## Key findings

- Daughter waves can be generated without satisfying the dispersion relation.
- Viscous dissipation broadens the transfer function bandwidth.
- Forced interactions significantly impact wave turbulence dynamics.

## Abstract

{Three-wave resonant interactions constitute an essential nonlinear mechanism coupling capillary surface waves. In a previous work, Haudin et al. [Phys. Rev E 93, 043110 (2016)], we have characterized experimentally the generation by this mechanism of a daughter wave, whose amplitude saturates due to the viscous dissipation. Here, we show experimentally the generation of a daughter wave verifying the resonant conditions, but not the dispersion relation.} By modeling the response of the free surface at the lowest nonlinear order, we explain this observation as a forced interaction. {The bandwidth of the linear transfer function of the free surface is indeed increased by the significant viscous dissipation.} The observation of free surface excitations not following the linear dispersion relation then becomes possible. This forced three-wave interaction mechanism could have important consequences for wave turbulence in experimental or natural systems with non negligible dissipation.