| Summary: | 博士 === 國立成功大學 === 水利及海洋工程學系碩博士班 === 95 === 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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