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工程力学  2014 

椭圆形港湾内水波共振的解析解

DOI: 10.6052/j.issn.1000-4750.2012.11.0886, PP. 252-256

Keywords: 港湾共振,椭圆形港湾,马丢函数,水波共振,海岸动力学

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Abstract:

通过坐标变换将线性长波方程转换为基于椭圆坐标系的水波运动方程,并采用分离变量法分别得到马丢方程描述的极角方向运动方程和拓展型马丢方程描述的径向运动方程。椭圆形港湾内的水波共振可以表示为马丢函数与拓展型马丢函数的乘积。由边界处自由水面法向量梯度为零求得水波共振的特征参数。椭圆形港湾内水波共振的极角方向波节点数与马丢函数的阶数相同,径向波节点数与边界条件相关。

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