This work presents Direct Numerical Simulations of capillary wave turbulence
solving the full 3D Navier Stokes equations of a two-phase flow. When the
interface is locally forced at large scales, a statistical stationary state
appears after few forcing periods. Smaller wave scales are generated by
nonlinear interactions, and the wave height spectrum is found to obey a power
law in both wave number and frequency in good agreement with weak turbulence
theory. By estimating the mean energy flux from the dissipated power, the
Kolmogorov-Zakharov constant is evaluated and found to be compatible with the
exact theoretical value. The time scale separation between linear, nonlinear
interaction and dissipative times is also observed. These numerical results
confirm the validity of weak turbulence approach to quantify out-of equilibrium
wave statistics.Comment: Physical Review Letters (2014) in pres
