Simulation of Capillary Wave Turbulence on the Basis of Fully Nonlinear Plane-Symmetric Model

Abstract

A new model for the direct numerical simulation of capillary wave turbulence arising at a free surface of deep incompressible fluid is proposed in the work. The plane-symmetric model based on the time-dependent conformal transform is fully nonlinear and takes into account the effects of surface tension, external random forcing and dissipation of energy. The simulation results show that the system of nonlinear capillary waves can go into a quasi-stationary state (wave turbulence regime), when the action of an external force is compensated by the viscosity. In this regime, the fluid motion demonstrates quite complex and irregular behavior. The spatial and frequency spectra of surface perturbations acquire a power-law dependence in the quasi-stationary state. The exponents of the spectra do not coincide with the classical Zakharov-Filonenko spectrum obtained for isotropic capillary turbulence. In the case of anisotropic quasi-1D geometry, five-wave resonant interactions become the dominant process. The numerical results agree with high accuracy with the corresponding analytical spectra obtained on the basis of dimensional analysis of weak turbulence spectra.