## Nonlinear interactions and turbulence of capillary surface waves

The dynamics of the waves propagating on a water surface is often

influenced by nonlinear effects. The complex and disordered patterns of

gravity waves seen on a choppy sea are indeed interpreted as a

statistical dynamic equilibrium of waves in interaction. Using among

some others the hypothesis of weak non linearity (small deformation of

the free-surface), the wave turbulence theory describes analytically

these states. When the surface tension is the main restoring mechanism,

the surface waves are called capillary waves and their wavelengths are

of scale of the centimeter or smaller. Nonlinear interactions and

turbulence of capillary waves are reported, but a major difference with

the large scale gravity waves consists in the significant viscous

dissipation in the propagation of capillary waves. In this seminar,

based on the analysis of several experimental works, we show that the

dissipation has important consequences on the nonlinear dynamics of

capillary waves. First, by increasing the width of the dispersion

relation, the contribution of non-resonant interactions is enhanced.

Then, large enough wave amplitudes are required for the nonlinear

effects to overcome the dissipation. Consequently, the turbulent states

of capillary waves correspond to strongly nonlinear regimes, beyond the

wave turbulence theory.