Abstract: We report on direct
numerical simulation of quasi-one-dimensional bidirectional
capillary-wave turbulence. Although nontrivial three-wave and
four-wave resonant interactions are absent in this peculiar
geometry, we show that an energy transfer between scales still
occurs concentrated around the linear dispersion relation that
is broadened by nonlinearity. The wave spectrum displays a clear
wave number power-law scaling that is found to be in good
agreement with the dimensionally prediction for capillary-wave
turbulence involving four-wave interactions. The carried out
high-order correlation analysis (bicoherence and tricoherence)
confirms quantitatively the dominant role of four-wave
quasi-resonant interactions. The Kolmogorov-Zakharov spectrum
constant is also estimated numerically. We interpret our results
as the first numerical observation of anisotropic capillary-wave
turbulence in which four-wave interactions play a dominant role.