波浪通過泥質底床上之水面結構物的理論分析

Analysis of waves passing through a surface structure on a muddy seabed

張振緯(Chen-Wei Chang)

指導教授 ： 詹益齊

國立臺灣大學/工學院/土木工程學研究所/碩士(2021年)

https://doi.org/10.6342/NTU202104449

摘要

水面結構物早已被廣泛運用於海事工程，但對於水面結構物的研究多半忽略泥床的影響以簡化問題。本文以解析解的方式，分析週期波通過泥質底床上方時，波浪、泥床與水面結構物三者的相互影響。
首先將邊界層等級厚度的泥質底床代入史托克動量方程式，得到水與泥質底床的速度關係式做為水域的下邊界條件，再使用特徵函數展開法求解水域勢能函數，得到在波浪、泥床與水面結構物三者交互作用下的水域勢能函數。
由於同時探討波浪、泥床與水面結構物三者相互影響的相關文獻十分稀少，本文與Ijima et al. (1970)和Mei and Black (1969)驗證無底泥情況的波浪散射行為，證明本研究有能力包含無泥散射行為。再與Ng (2000)驗證波浪通過泥質底床時的衰減係數與中間波波高，證明本研究有能力包含單純波浪通過泥床問題。最後與鄭 (2021)的數值模擬比較自由液面波高、速度頗面、速度時間序列與縱向力時間序列，分析數值模擬與理論解析的成果。
對波浪而言，隨著底泥厚度的增加，透射係數也隨之增加、反射係數則隨之減少。邊界層等級厚度的底泥對波浪的散射行為影響不超過百分之一，可以考慮忽略薄底泥對散射行為的影響，但在大尺度問題下，需要考慮波浪的衰減行為。對水面結構物而言，增加底泥厚度會使結構物所受壓力與縱向力減少，推測是因為泥床吸收能量導致，並且以結構物中心偏向堤前的位置壓力減少幅度最大。對泥床而言，中間波波高大小取決於結構物下方的能量通量與板長，能量通量越大，中間波波高越大。而適當的板長能增加能量對底泥的擾動，但若板長過長會抑制能量通過結構物，從而減少中間波波高。

關鍵字

週期波 ； 泥床 ； 解析解 ； 特徵展開法 ； 水面結構物

並列摘要

Surface structures have long been widely used in maritime engineering, but most studies on surface structures ignore the influence of mud beds to simplify the problem.This paper analyzes the interaction between waves, mud beds and water surface structures when periodic waves pass through the muddy bed by means of analytical solutions.
First, the muddy bed with the thickness of the boundary layer is substituted into the Stokes momentum equation, and the velocity relationship between water and muddy bed is obtained as the lower boundary condition of the water area, and then the eigenfunction expansion method is used to solve the potential energy function of the water area to obtain The potential energy function of the water area under the interaction of waves, mud beds and water surface structures.
Since the related literatures discussing the interaction of waves, mud beds and water surface structures at the same time are very rare, this paper verify the wave scattering behavior without muddy bed with Ijima et al. (1970) and Mei and Black (1969) to prove this research ability to include scattering behavior without muddy bed. Then verify with Ng (2000) the attenuation coefficient and the intermediate wave height when the wave passes through the muddy bed, which proves that this study is capable of including the wave passing through the mud bed. Finally, it compares the free surface wave height, velocity, velocity time series and longitudinal force time series with Zheng (2021) numerical simulation, and analyzes the results of numerical simulation and theoretical analysis.
For waves, as the thickness of the muddy bed increases, the transmission coefficient also increases and the reflection coefficient decreases.The muddy bed with the boundary layer thickness does not affect the scattering behavior of waves by more than one percent, and the influence of thin muddy bed on the scattering behavior can be ignored. However, for large-scale problems, the wave attenuation behavior needs to be considered. For water surface structures, increasing the thickness of the muddy bed will reduce the pressure and longitudinal force on the structure, presumably because the mud bed absorbs energy, and the pressure at the position where the center of the structure is deviated from the front of the embankment has the largest decrease. For mud beds, the middle wave height depends on the energy flux under the structure and the plate length. The greater the energy flux, the greater the middle wave height. The appropriate length of the plate can increase the energy disturbance to the bottom mud, but if the length of the plate is too long, it will inhibit the energy from passing through the structure, thereby reducing the intermediate wave height.

並列關鍵字

periodic wave ； mud bed ； analytical solution ； eigenfunction expansion method ； surface structure

參考文獻

Bai, K. J. (1975). Diffraction of oblique waves by an infinite cylinder. Journal of Fluid Mechanics, 68(3), 513-535.

Bolton, W., Ursell, F. (1973). The wave force on an infinitely long circular cylinder in an oblique sea. Journal of Fluid Mechanics, 57(2), 241-256.

Dalrymple, R. A., Liu, P. L. F. (1978). Waves over Soft Muds: A Two-Layer Fluid Model. Journal of Physical Oceanography, 8(6), 1121-1131. https://doi.org/10.1175/1520-0485(1978)008<1121:Wosmat>2.0.Co;2

Dean, R. G., Ursell, F. (1959). Interaction of a fixed, semi-immersed circular cylinder with a train of surface waves. Massachusetts Institute of Technology, Hydrodynamics Laboratory.

Dean, W. R. (1945). On the reflexion of surface waves by a submerged plane barrier. Mathematical Proceedings of the Cambridge Philosophical Society, 41(3), 231-238. https://doi.org/10.1017/S030500410002260X