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上结构的非线性响应起着至关重要的作用。在高于3^<rd>阶的情况下，对它们的理论估计尚未建立。这主要是因为在摄动方法下，长期项出现在自由曲面条件下。Molin表明，数值滤波可以有效地避免这些问题，但他的方法不适用于浅水的问题。本文给出了浅水中作用在圆柱上的3^<rd>阶波浪力的公式，并研究了其长期项的一般数学行为。长期术语的另一个重要而有趣的问题是波漂移附加质量，它对于估计系泊浮体在不规则波浪中的慢漂移振荡以及波漂移阻尼是非常重要的。我们用扰动法用两个小参数（波斜率和运动频率）表示了这个问题。长期项出现在高阶问题中，类似于3^<rd>阶波力问题。我们首先得到了设置唯一解的辐射条件。将所得溶液与新研制的实验装置的实测数据进行了比较。

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.