  We study experimentally the dynamics and statistics of capillary waves forced
by random steep gravity waves mechanically generated in laboratory. Capillary
waves are produced here by gravity waves from nonlinear wave interactions.
Using a spatio-temporal measurement of the free-surface, we characterize
statistically the random regimes of capillary waves in the spatial and temporal
Fourier spaces. For a significant wave steepness ($0.2-0.3$), power-law spectra
are observed both in space and time, defining a turbulent regime of capillary
waves transferring energy from large scale to small scale. Analysis of temporal
fluctuations of spatial spectrum demonstrates that the capillary power-law
spectra result from the temporal averaging over intermittent and strong
nonlinear events transferring energy to small scale in a fast time scale, when
capillary wave trains are generated in a way similar to the parasitic capillary
wave generation mechanism. The frequency and wavenumber power-law exponents of
wave spectrum are found to be in agreement with those of the weakly nonlinear
Wave Turbulence Theory. However, the energy flux is not constant through the
scales and the wave spectrum scaling with this flux is not in good agreement
with Wave Turbulence Theory. These results suggest that theoretical
developments beyond the classic Wave Turbulence Theory are necessary to
describe the dynamics and statistics of capillary waves in natural environment.
In particular, in presence of broad scale viscous dissipation and strong
nonlinearity, the role of non-local and non-resonant interactions could be
reconsidered.
