The seiche motion induced in a partially open harbour is uniquely determined by the standing wave pattern formed in the outside ocean. The variable location and size of the coupling makes the problem essentially three-dimensional. Existing potential theory has been extended, for the case of a simple rectangular port, to simulate ocean conditions by approximating the open ocean by another rectangular basin of large size. The theoretical problem then reduces to solving the Neunan problem for the two-dimensional Helmholtz equation V*F + K*F m o for a polygonal contour. The finite dimensional approximation of an infinite domain is, however, unsatisfactory at least from the analytical point of view.This difficulty has been removed, in this paper, by using elliptic-cylindrical co-ordinates for the semi-infinite domain in which the perturbation potential has been expanded in terms periodic Mathieu functions. These theoretical developments have been verified by a series of numerical calculations and experimental studies.
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机译：在部分开放的港口中引起的seiche运动是唯一由外部海洋中形成的驻波图确定的。联轴器的可变位置和大小使问题基本上是三维的。对于简单的矩形港口，现有的势能理论已经得到扩展，可以通过用另一个大尺寸的矩形海盆逼近开阔的海洋来模拟海洋条件。然后，理论问题简化为求解多边形轮廓的二维Helmholtz方程V * F + K * F m o的Neunan问题。然而，至少从分析的角度来看，无限域的有限维逼近是不令人满意的。本文通过将椭圆柱坐标用于半无限域来解决了这一难题，该半无限域在其中周期性Mathieu函数的潜力得到了扩展。这些理论发展已通过一系列数值计算和实验研究得到验证。
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