Numerical studies on wave forces and moored ship motions in intermediate and shallow water
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- Institutt for marin teknikk 
Wave forces and motions of a moored ship in intermediate and shallow water depth are investigated numerically in the present thesis. The studies are carried out in the framework of potential flow theory. Three numerical models, which include a 2D and 3D fully nonlinear numerical wave tank (FNWT), a second-order perturbation method and a coupled Boussinesqpanel model, are developed and verified by available theoretical and experimental results. In the FNWT, numerical issues like accurate tracking of the interaction lines between different boundary surfaces, regridding of the free surface and body surface, and solving the time derivative of the velocity potential are handled efficiently. The code is paralleled and therefore it can sufficiently take advantage of the computational resources. A series of verifications and validations, which include nonlinear wave simulations, radiation problems and diffraction problems, are performed to demonstrate the accuracy and robustness of the FNWT. The influences of the water depth on the hydrodynamic forces and the corresponding motions of a moored ship are investigated. The significant effects of the water depth on the horizontal hydrodynamic forces and ship motions are highlighted. In addition, transient effects last long in the simulated surge of a moored ship in head waves. Using a ramp function to start the simulations smoothly and introducing a small surge damping, which may be due to viscous hull and mooring lines in reality, can suppress transient effects efficiently. One main shortcoming of the FNWT is the low computational efficiency. To study the wave drift forces on a moored ship in non-shallow water in a more efficient way and analyze the relative importance of different components, a second-order perturbation model using the wave steepness as a small parameter is developed and implemented. According to our numerical tests, wave drift forces on a moored tanker in head waves have distinct increments in shallower water depth. Further, the different components in the wave drift forces are analyzed and it is found that the second-order velocity potential, whose contribution is very small in deep water, gives a dominant contribution in shallow water. Thus, Newman’s approximation, in which the secondorder velocity potential is neglected, significantly under-predict the slow-drift excitation forces in shallow water. However, the results tend to be over-predicted by Pinkster’s approximation, which only considers the second-order components in the incident waves. The topographies in offshore area are usually complex and far different from horizontal bottom, on which the analytical Stokes theory is based. To incorporate the influences of the bottom topography efficiently, a coupled Boussinesq-panel model is then developed and examined. Incident waves are generated by the Boussinesq model (BM), which can accurately describe the diffraction, refraction and reflection in complicated topographies. The scattered velocity potential due to a floating body is solved by a linear panel model. Only the nonlinear components in the incident waves are incorporated while the nonlinear interactions between incident waves and scattered waves are neglected. Numerical tests show that the BM can describe incident waves in complex topography quite accurately. Moreover, the ‘set-down’ phenomenon in irregular waves is also captured well by the BM. At last, it is found that the root mean square values of the slowly-varying surge motions of a moored tanker in irregular head waves by the coupled model are larger than that predicted by the complete second-order perturbation method and the FNWT, but are still in the same magnitude.