Phase velocity effect of nonlinear interactions between surface gravity waves in finite water depth

The phase velocity of surface waves can be significantly affected by the nonlinear wave interactions, but the behavior of this problem in finite water depth has not been well understood. To better understand the effect of water depth on the variation of phase velocities, we perform theoretical analysis and direct numerical simulations using higher-order spectral method. Through both analytical and numerical analyses, we find the threshold value of water depth where the nonlinear effects on phase velocity disappear. The effect of crossing angle on the nonlinear wave interactions is also discussed.