Simulation of the Wave Turbulence of a Liquid Surface Using the Dynamic Conformal Transformation Method

Abstract: The dynamic conformal transformation method has been generalized for the first time to numerically simulate the capillary wave turbulence of a liquid surface in the plane symmetric anisotropic geometry. The model is strongly nonlinear and involves effects of surface tension, as well as energy dissipation and pumping. Simulation results have shown that the system of nonlinear capillary waves can pass to the quasistationary chaotic motion regime (wave turbulence). The calculated exponents of spectra do not coincide with those for the classical Zakharov-Filonenko spectrum for isotropic capillary turbulence but are in good agreement with the estimate obtained under the assumption of the dominant effect of five-wave resonant interactions.