椭圆余弦波的位移法分析

Analysis on cnoidal wave using displacement method

为研究线性浅水波理论的适用范围,基于位移浅水波方程的椭圆余弦波解,计算在不同水深h、波高η0和波长L条件下,非线性椭圆余弦波与线性余弦波的相对差。数值计算结果表明:η_0/h越小或h/L越大,浅水波的非线性效应越弱;当η_0≤0.42h且η_0L^2/h^3≤5.34-12.85η_0/h时,非线性椭圆余弦波与线性余弦波的相对差小于0.05,可满足工程需要。

To study the scope of linear shallow water wave theory,the relative difference between nonlinear cnoidal wave and linear cnoidal wave is calculated by the cnoidal wave solutions of displacement shallow water equation in different water depth h,wave height η0 and wave length L. The numerical calculation results show that,the nonlinear effect of shallow water wave declines when η0/h decreases or h/L increases; the relative difference of nonlinear and linear cnoidal wave is less than 0. 05 when η0≤0. 42 h and η0 L^2/h^3≤5. 34-12. 85η0/h,which can satisfy the engineering requirement.