Theory of non-linear wave forces acting on an offshore structure in a shallow water and comparison with experiments

非线性波浪力对张力腿平台等海洋结构物的非线性响应起着至关重要的作用。在高于3阶的情况下，理论上估计它们还没有建立<rd>。这主要是因为在摄动法中，自由表面条件下出现了长期项。莫林表明，数值滤波是有用的，以避免他们，但他的方法不能适用于问题的情况下，浅水。本文建立了<rd>作用在浅水中圆柱上的三阶波浪力公式，并研究了长期项的一般数学行为。长期项的另一个重要和有趣的主题是波浪漂移附加质量，这对于估计系泊浮体在不规则波中的慢漂移振荡以及波浪漂移阻尼非常重要。我们已经制定了两个小参数，这是波的斜率和运动频率的摄动方法的问题。与3阶波浪力问题类似，高阶问题中也出现了长期<rd>项。我们首先得到了辐射条件，以设置唯一的解决方案。所得到的解决方案进行了比较，通过新开发的实验装置获得的测量数据。

Non-linear wave forces act essential role on non-linear responses of an offshore structure such as a tension leg platform. It has not been established yet to theoretically estimate them in case of higher than 3^<rd> order. It is mainly because of secular terms which appear in a free-surface condition in case of perturbation approach. Molin shown that numerical filtering is useful to avoid them, but his method cannot apply to the problem in case of shallow water. In this research we have formulated 3^<rd> order wave force acting on a circular cylinder in shallow water, and studied general mathematical behavior of the secular terms. Another important and interesting subject of a secular terms is a wave drift added mass, which is very important to estimate slow drift oscillation of a moored floating body in irregular waves, as well as a wave drift damping. We have formulated the problem by a perturbation method with two small parameters which are wave slope and motion frequency. Secular terms appear in the higher order problems, similarly to the 3^<rd> order wave force problem. We have firstly obtained radiation conditions to set unique solutions. The obtained solutions were compared with the measured date obtained by newly developed experimental set-up.