This paper proposes a 3-D non-hydrostatic free surface flow model with a newly proposed general boundary-fitted grid system to simulate the nonlinear interactions of the bi-chromatic deep-water gravity waves. First, the monochromatic bidirectional and bi-chromatic bidirectional waves of small wave steepness are successively simulated to verify the abilities of the numerical model. Then, a series of bi-chromatic progressive waves of moderate wave steepness and different crossing angles are simulated and analyzed in detail. It is found that if the crossing angle is close to or smaller than the resonant angle, apparent discrepancies are observed among the numerical results, the linear wave theory, and the steady third-order theory. Otherwise, the three solutions coincide well. Through analysis, it is concluded that the discrepancies are caused by the third-order quasi-resonant interactions between the bi-chromatic progressive waves. Such interactions not only could modify the wave spectrum, but could also change the wave shape patterns.

本文提出了一种具有新提出的通用边界拟合网格系统的 3-D 非静水自由表面流动模型，以模拟双色深水重力波的非线性相互作用。首先，依次模拟了小波陡度的单色双向波和双色双向波，以验证数值模型的能力。然后，对一系列中等波陡度和不同交叉角的双色渐进波进行了详细的模拟和分析。发现如果交叉角接近或小于共振角，数值结果、线性波理论和稳态三阶理论之间会出现明显的差异。否则，这三个解决方案很好地吻合。通过分析，得出的结论是，这种差异是由双色渐进波之间的三阶准共振相互作用引起的。这种相互作用不仅可以修改波谱，还可以改变波形模式。