The Dynamic Response of a Moored Vessel in Shallow Water Using Boussinesq Equations

In this study, firstly nonlinear waves in shallow water were simulated by using the Boussinesq equations. The simulated waves represented well the wave deformations such as shoaling and refraction as well as non-linear wave interactions among wave components as they approach coastal region from far field. The velocity components of the simulated waves at an arbitrary location in the fluid domain can be computed most effectively by introducing the so-called utility velocity. By taking the deformed wave field into account, the motion response of a moored floating barge was analyzed. The wave excitation and radiation force were estimated by the Constant Panel Method (CPM) based on linear potential theory. In order to estimate the wave excitation force including shallow water effects, the wave height and the wave velocity components obtained from the Boussinesq simulation were used. This approach used to estimate the wave excitation force including shallow water effects is herein referred to as Hybrid Boussinesq-CPM. An example calculation was made for the Pinkster barge, which is supposed to be located in a specific bottom topography and moored by the Tower Yoke Mooring System. The results were compared with those obtained for the equivalent constant water depth condition. The comparison showed that the motion responses obtained by the Hybrid model were larger than those for the even bottom case. In particular, the horizontal surge motion was significantly enlarged because of two facts: the wave deformation due to the bottom topography and the low frequency waves caused by nonlinear wave-wave interactions. The enlarged horizontal surge motion is important for mooring design in shallow water.