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。 The linear wave equation is converted into a wave equation of motion based on the elliptic coordinate system by coordinate transformation, and the equations of motion of the polar angle and the equations of motion described by the extended equation are respectively obtained by the method of discrete variables. The wave resonance in elliptical harbor can be expressed as the product of the horse throwing function and the extended horse throwing function. The characteristic parameters of water wave resonance are obtained from the normal vector gradient of free surface at the boundary. The number of polar wave nodes in the water wave resonance in the oval harbor is the same as that of the horse throw function, and the number of radial wave nodes is related to the boundary conditions.