短波与长波的非线性作用及其对大尺度物体的波浪荷载

THE NONLINEAR INTERACTION OF SHORT WAVES AND LONG WAVES AND ITS LOADS ON LARGE STRUCTURE

本文用多重尺度法研究了短波在长波上行进时的波浪场,解得有限水深时弱非线性作用下短波波幅的变化规律。当上述波列入射到大尺度结构上时,发生了具有缓变调制的群波绕射问题。整个问题可分为三个定解问题:一阶一次谐波绕射的定解问题用线性绕射理论求解;二阶一次谐波绕射问题是本文研究的重点,它可以分成三个部分,其中一个是满足泊松方程的解,另两个是满足拉普拉斯方程分别具有齐次与非齐次自由表面边界条件的解;二阶二次谐波绕射的定解问题采用文献[4]的方法求解。本文计算了不同长波波长情况下二阶共同作用荷载,与单纯二阶波浪荷载比较,得出了短波和长波相互作用对荷载的影响。

The mechanism of nonlinear interaction of short waves and long waves has been investigated in this paper. The hydrodynamic forces on a large structure due to short waves and long waves have been obtained by using Boundary Element Method. The solution of excited forces due to those combine short waves upon a large body can be divided into three parts which are solved by different methods. The first one, the first-harmonic scattering velocity potential at first order is solved by linear diffraction theory. The second one, the first-harmonic scattering velocity potential at second order is composed of three parts. One satisfies the Poisson Equation and the other two satisfy the Laplace Equation with homogeneous and inhomogeneous free surface boundary condition respectively. The third one, the second-harmonic scattering at second order, is solved