本研究主要目的為開發三維數值黏性造波水槽，並利用此水槽探討波浪與近岸結構物之交互作用。數值波浪水槽之數學模式主要是求解三維時變的Navier-Stokes方程及非線性的自由液面邊界條件。計算域上游設有一造波板，用以製造出所欲模擬之波形，包括微小振幅波、有限振幅波及孤立波；而下游則設有一海棉層（sponge layer）用來消散波浪，減少波浪的反射。在數值方法上，本研究應用有限解析法離散偏微分方程，且改進MAC (marker-and-cell)法處理三維自由液面。由於三維計算所需記憶體及計算時間皆相當龐大，本研究所有的計算均在聯結多台電腦所構成的叢集電腦上執行。編寫平行化程式及執行平行計算所使用的語言為MPI(Message Passing Interface)及平行計算軟體MPICH。為了驗證數值方法的正確性，本研究利用此三維造波水槽模擬孤立波的生成及傳遞，數值計算所得波形、流場速度及波高衰減，皆與理論結果非常吻合。此外，並模擬孤立波及規則波通過半無限長防波堤的繞射現象，數值結果經與理論解及實驗結果比較，有很好的一致性。
在驗證了本數值波浪水槽的正確性及可信度之後，本研究探討孤立波與三維潛堤之交互作用。孤立波通過三維潛堤所產生的波浪變形、渦流及潛堤附近流體質點的軌跡，文中做了有系統的分析。為了突顯潛堤寬度的影響，本研究探討兩個不同寬度的三維潛堤及一個二維潛堤。數值結果顯示在相同潛堤高度下，由二維潛堤所造成的反射波遠大於三維潛堤的結果，而三維潛堤所造成的透射波遠大於二維潛堤的結果，即使是在潛堤正後方的部份。當孤立波通過三維潛堤時，在近底床的每個堤角處均有渦流的產生，於實際應用上可能造成嚴重的沖刷問題。此外，為了瞭解三維潛堤附近複雜的流場變化，本研究也仔細分析潛堤附近流體質點的軌跡，並發現其變化與速度場一致。
本數值波浪水槽亦應用於研究規則波與潛堤的互制作用。不同潛堤寬度對波形演變、潛堤附近的繞射係數、潛堤堤角的流離現象及渦流生成做了有系統的研究。潛堤上方的複雜流場由潛堤前方的透射波、潛堤兩側及潛堤後方的折射波及透射至下游所造成的負反射波所構成。當潛堤的寬度較小時，這些效應將合併導致潛堤上方的凸起部份較高。繞射係數在空間的分佈顯示波浪通過二維潛堤有較好的遮蔽效果。在同樣的潛堤高度下，在三維潛堤正後方的波浪振幅變大，顯示在三維潛堤後方是不良的保護區域，反而在三維潛堤兩側的後方存在著低繞射係數的區域。此外，研究結果顯示三維潛堤附近渦流的生成，只有在特定的時間及剖面才會發生。潛堤後方的流場會因為透射波及繞射波的疊加效應而增強，導致有著較嚴重的沖刷問題。

The purpose of this study is to developed a three-dimensional (3D) numerical viscous wave tank and apply it to study the interaction of water waves and marine structures. A numerical scheme is developed to solve the unsteady 3D Navier-Stokes equations and the fully nonlinear free surface boundary conditions for simulating a 3D numerical viscous wave tank. The finite-analytic method was used to discretize the partial differential equations, and the marker-and-cell (MAC) method was extended to treat the 3D free surfaces. A piston-type wavemaker was incorporated in the computational domain to generate the desired incident waves, including the small- and finite-amplitude waves and the solitary waves. All the computations in this study were carried out by a PC-cluster established by connecting several personal computers. The Message Passing Interface (MPI) parallel language and MPICH software were used to write the computer code for parallel computing. In order to verify the accuracy of the numerical scheme, the numerical scheme was applied to simulate the generation and propagation of a solitary wave in the wave tank. The numerical results of the wave profile, velocity fields and the wave height attenuation were found to be in good agreement with the theoretical solutions. The accuracy of the 3D wave tank model was also confirmed by simulating the propagation of a solitary wave and periodic waves over a semi-infinite breakwater.
After having verified the accuracy of the 3D Wave tank model, this model was applied to study the interaction of a solitary wave and a submerged 3D breakwater. Characteristics of the wave and flow fields were discussed in terms of wave transformation, vorticity and trajectories of fluid particles around the breakwater. Two cases of 3D breakwater with different aspect ratios and one 2D breakwater were investigated. The numerical results showed that under the same breakwater height, the reflected waves caused by a 2D breakwater are much larger than those caused by 3D breakwaters, and the transmitted waves of the 3D breakwater are larger than those of the 2D breakwater, even at the region right behind the breakwater. When a solitary wave passes the 3D breakwater, vortices form at each corner of the breakwater near the bottom, they may cause severe scouring problem in real applications. For 3D breakwaters, due to the side-end effect, the reverse flow induced by the negative water surface elevation also causes a strong reverse flow at the left top of the breakwater, diminishing the streamwise flow velocity there. The trajectories of particles are determined to better understand the 3D time-dependent flow structure near the breakwater. These trajectories are shown to be consistent with the velocity fields.
The numerical wave tank was also applied to simulate the propagation of periodic waves over a submerged breakwater. Effects of different width of the breakwater on the wave transformation, the diffraction coefficient around the breakwater, flow separation at the corners of the breakwater, and the vortex generation were studied systematically. The complex flow field above the breakwater is constituted by transmitted waves from the weather side of the breakwater, the refracted waves from the lateral sides of the breakwater and the diffracted wave from the lee side of the breakwater as well as the reflected wave from the lee side edge of the breakwater. As the width of the breakwater is smaller, these components combined to lead the peak above the breakwater higher. The distribution of diffraction coefficient in space shows good shelter effect as waves over a 2D case. Under the same breakwater height, the wave amplitude at the lee side of the 3D breakwaters is strengthened which shows right behind 3D submerged breakwaters is not the best protection region. Inversely, small diffraction coefficients exist behind the lateral sides of the 3D breakwaters. Numerical results show also that the vortex may occur at some times and at some positions. The intensity of the flow field at the lee side of the breakwater is stronger caused by the transmitted waves and diffracted waves overlapped to lead serious scouring problem, which may more complex and more serious than the result by solving a 2D problem.

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