弱非线性调制水波与垂直桩柱间的二阶相互作用

The Second Order Interaction Between the Weakly Nonlinear Waves and a Vertical Cylinder in Slightly Modulated Beam Sea

采用多重尺度展开方法，提出了一个具有缓慢调制的弱非线性水波与垂直桩柱间的二阶相互作用理论，导出了平均流动散射势的演化方程及一次散射波包络的演化方程，给出了二阶绕射势的解和二阶波力的表式．此外，还揭示出：平均流动散射势的远方行为相当于以浅水波速径向朝外传播的波系，而一次散射波调制包络的演化规律与入射波调制包络的演化规律相同。

In this paper,with the multiple scale perturbation expansion method,a second order theory on the interaction between the weakly nonlinear modulated water waves and vertical cylinder is developed.The evolution equations of the second order scattered set down waves and the envelope of the first order scattering waves have firstly been derived,and then the second order solution of the diffraction potential and the expression of the second order wave loads have been obtained.It is found that the scattered set down waves propagate outward in the radial direction and the modulated waves for the first order scattering waves also propagate outward in the radial direction but with the group velocity and with the long wave speed respectively.