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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。
In this paper, the multi-scale method was used to study the wave field when the shortwave was traveling on the longwave, and the variation law of the shortwave amplitude under the weak nonlinearity was obtained when the water depth was limited. When the above wavelets are incident on a large-scale structure, a group wave diffraction problem with a slow modulation occurs. The whole problem can be divided into three fixed solutions: the first-order harmonic diffraction problem is solved by linear diffraction theory; the second-order harmonic diffraction problem is the focus of this paper, which can be divided into three parts, One is to satisfy the solution of the Poisson equation and the other two to satisfy the Laplace equation with homogeneous and nonhomogeneous free surface boundary conditions respectively. The second-order second harmonic diffraction problem is solved by the literature [ 4] method to solve. In this paper, the second-order co-acting loads with different long-wavelength wavelengths are calculated. Compared with the simple second-order wave loads, the effect of short-wave and long-wave interaction on the load is obtained.