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

非线性波浪力对海洋结构物(如张力腿平台)的非线性响应起着至关重要的作用。对于高于3^RD&>订单的情况，从理论上估计它们还没有建立起来。这主要是因为在摄动法的情况下，长期项出现在自由面条件下。莫林表明，数值滤波可以有效地避免它们，但他的方法不适用于浅水情况下的问题。在这项研究中，我们建立了作用在浅水中圆柱上的三阶波浪力的公式，并研究了长期项的一般数学行为。另一个重要而有趣的长期课题是波浪漂移附加质量，它对于估算系泊浮体在不规则波中的缓慢漂移振荡以及波浪漂移衰减是非常重要的。我们用两个小参数，即波浪斜率和运动频率，用摄动法来描述问题。长期项出现在高阶问题中，类似于3阶波浪力问题。我们首先得到了辐射条件，以设置唯一的解。将得到的解与新开发的实验装置所获得的测量数据进行了比较。

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.