博士 / 國立成功大學 / 水利及海洋工程學系碩博士班 / 92 / The unsteady two-dimensional Navier-Stokes equations and Navier-Stokes type model equations for porous flows were solved numerically to simulate the propagation of water waves over a permeable bed, a submerged porous breakwater, and a rippled porous bed. The Navier-Stokes type model equations for the flow inside the porous structure are complete, containing the convective inertial force term and the viscous force term, both terms are often ignored in the previous literature. The free surface boundary conditions and the interfacial boundary conditions between the water and the porous media are in complete form. A piston-type wavemaker was set-up in the computational domain to generate the incident waves, including the small- and finite- amplitude waves as well as the solitary waves.
To demonstrate the proposed model equations are suitable for investigating the interaction of waves and porous offshore structure, first of all, the proposed model equations are solved numerically to simulate the propagation of water waves over a porous bed. The numerical results for the free surface elevation, the velocity profile near the interface, and the pore pressure in the porous bed are in good agreement with available experimental data and analytical solutions. After having verified the accuracy of the numerical scheme, effects of different parameters on the propagation of periodic waves and solitary waves over a porous bed are investigated. Our numerical results showed that the effective thickness of the boundary layer above the porous bed depends on the porosity and permeability. In the investigated cases, the thickness can reach as high as 50 , while the corresponding value for impermeable bed is 10 . For porous bed with large porosity and permeability, the effective thickness of Brinkman’s viscous layer depends not only on the porosity and permeability, but also on the wave phase due to the effect of the inertial force from the upper water region. In the investigated cases, the effective thickness varies between 0 and 20 .
The propagation of periodic waves over a rectangular permeable breakwater was then studied. The numerical results of the wave profiles recorded at several stations near the breakwater were compared with the experimental results to verify the accuracy of the numerical scheme. Spatial evolution of higher harmonics as waves propagate over a breakwater was determined. The transformation of waves near the breakwater was discussed in terms of the beat length of the higher harmonics and the energy transfer between the bound waves and free waves. The variation of the reflection and transmission coefficient with respect to the width of the breakwater was also determined. The flow fields near the breakwater are discussed in terms of the velocity vectors, the circulation, and the trajectories of the fluid particles. The pressure drag acting on the breakwater was also calculated. The propagation of a solitary wave over a porous breakwater was also investigated. Our numerical results reveal that if the breakwater width is small compared with the effective wavelength, the structure permeability has no apparent effect on wave transformation. For wide porous breakwaters, if the structure porosity is small, the increase in the porosity results in the reduction of the transmission coefficient; otherwise the transmission coefficient increases with porosity.
A numerical scheme was also developed to solve the Navier-Stokes model equations and the exact free surface and interface boundary conditions to study the propagation of water waves over artificial rippled porous beds. A boundary-fitted coordinate system was used in this model. The accuracy of the numerical scheme was verified by comparing the numerical results for the spatial distribution of wave amplitudes on the impermeable and permeable rippled bed at resonant conditions with the analytical solutions. For the periodic incident waves, the flow field over the wavy wall is discussed in terms of the steady Eulerian streaming velocity. To provide information for understanding the possible mechanism of sediment transport around the rippled bed, trajectories of the fluid particles with initial locations close to the ripples were determined. One of our main results showed that under the action of periodic water waves, fluid particles on the impermeable rippled bed move at first back and forth around the ripple crest with increasing vertical distance from the ripple wall. After one or two wave periods they are then lifted up and shifted towards the next ripple crest. When the rippled bed is permeable, the size of the vortices generated at both the weather and lee sides of the porous ripples are smaller, because the flow is allowed to penetrate into or through the porous bed. All of the marked particles on the rippled porous bed shift onshore with much larger displacement than that in the impermeable case. The back and forth movement does not dominate the motion of the particles, except at the weather side of the ripple crest. The particles move rather straightforward in the wave direction.
| Identifer | oai:union.ndltd.org:TW/092NCKU5083006 |
| Date | January 2004 |
| Creators | Hsing-Han Chang, 張興漢 |
| Contributors | Hwung-Hweng Hwung, Ching-Jer Huang, 黃煌煇, 黃清哲 |
| Source Sets | National Digital Library of Theses and Dissertations in Taiwan |
| Language | en_US |
| Detected Language | English |
| Type | 學位論文 ; thesis |
| Format | 200 |
Page generated in 0.0078 seconds