Turbulence of Capillary Waves

A numerical model for direct simulation of the surface of ideal fluid based on the expansion of the Hamiltonian of the surface up to terms of fourth order is developed. For the case of capillary wave we observe the formation of powerlike spectrum of spatial elevations close to one predicted by weak-turbulent theory $I_k\simeq k^{-19/4\mathrm{}}$, which previously was not confirmed either experimentally or numerically.