圆柱形容器中自由表面波的非线性解

对圆柱形容器中的自由毛细重力表面波进行了摄动分析.采用毛细重力表面波的线性解作为本征函数,对自由面波高及速度势作Galerkin展开,根据Luke变分原理,导出了非线性自由毛细重力表面波的控制方程.使用多重尺度法导出了控制方程的前三阶摄动方程,在表面波列在无内共振情况下,求出了所讨论问题的三阶一致有效解,并且发现由于模态间的非线性相互作用,波的固有频率得到了修正.

Nonlinear Solutions of Free Surface-Waves in a Circular Cylindrical Basin

Perturbation analysis of free capillary-gravity surface-waves in a circular cylindrical basin is developed. The linear solutions of surface-waves in a basin are adopted as basis functions.By taking Galerkin's expansions of the velocity potential and the free surface elevation, the governing equations are derived from Luke's variational principle.The first three orders perturbation equations are obtained by use of expansion of multiple-scale.The first three orders valid solution of the problem is derived under the circumstance of no internal resonance inside the surface-waves.The initial natural frequencies of surface-waves are found to be modified because of nonlinear interactions among modes.