Direct numerical simulations of capillary wave turbulence

Abstract: 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.