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.

我们报告了准一维双向毛细管波湍流的直接数值模拟。尽管在这种特殊的几何结构中不存在非平凡的三波和四波共振相互作用，但我们表明，尺度之间的能量转移仍然集中在线性弥散关系附近，而线性弥散关系由于非线性而扩大。波谱显示出清晰的波数幂律定标，已发现与涉及四波相互作用的毛细管波湍流的尺寸预测非常吻合。进行的高阶相关分析（双相干和三相干）定量确定了四波准谐振相互作用的主导作用。Kolmogorov-Zakharov谱常数也可以通过数值估算。