礫石底床波浪變形之數值分析

Numerical Simulations of Wave Transformations over Gravel Seabed

林信宏(Hsin-Hung Lin)

指導教授 ： 林銘崇

國立臺灣大學/工學院/工程科學及海洋工程學研究所/碩士(2008年)

https://doi.org/10.6342/NTU.2008.00351

摘要

本文旨在應用考慮透水效應之布斯尼斯克方程式(Boussinesq equations)探討礫石底床對波浪變形之影響，理論模式方面以Cruz et al.(1997)所推導之以水深平均速度及水深平均滲流速度表示之布斯尼斯克方程式，並參考Madsen and Sørensen(1991)建議的方法，引入一與地形及淺化有關參數，可以將此方程式擴展至相對水深較深的區域。數值模擬計算則利用有限差分法之四階亞當斯-貝西福斯-摩頓之預測-修正法，配合使用造波函數與消波邊界條件，增加計算穩定性及節省計算時間。將所建立之數值模式與前人研究結果相互比較驗證後，模式的適用性相當良好。參考van Gent(1995)之研究，利用一與礫石之中值粒徑及孔隙率相關之滲透性係數模擬礫石底床之特性，並觀察其瞬時水位及波高分佈情形，探討波浪通過礫石底床之變化。由計算之結果可知，礫石底床可有效的消減波浪之波高，於本研究之計算條件：入射周期T=6.2及7.5秒於等水深h/L=0.094及0.076及變水深h/L=0.197~0.052及0.153~0.043之情況下，波浪通過180m長、孔隙率λ=0.442且kp=2.23×10-7 m2之礫石底床約可消減約20％之波高；其次也可得知本研究利用滲透性係數kp配合孔隙率模擬礫石底床之特性相當合理。

關鍵字

礫石底床 ； 布斯尼斯克 ； 滲透性係數

並列摘要

The purpose of this research is to investigate wave deformations passing through the gravel seabed by applying the Boussinesq equations. The theoretical model is based on the Boussinesq equation demonstrated by Cruz et al. (1997), expressed by depth-averaged velocity and depth-averaged seepage velocity. Madsen and Sørensen (1991) introduce a parameter related with shoaling and topography, to improve the dispersion for a large relative depth, h/L. The numerical model uses the Fourth-Order Adams-Bashforth-Moulton Predictor-Corrector Scheme and is coupled with source function and absorbing boundary condition to increase the stability of calculation and to decrease the required processing time. The results are quite well in comparison with forerunners’ researches. This research applied the intrinsic permeability related with the porosity and the mean size of the porous material, proposed by van Gent(1995), to express the property of gravel seabed. The wave transformations with waves passing through the gravel seabed is studied by observing the distributions of the surface elevations and wave heights. From the numerical results shown, that the gravel seabed could efficiently decay the wave height. The numerical experiments with wave pass through the constant water depth and varying depths are examined. The incident wave periods are T=6.2 and 7.5 sec. The parameter, h/L, are 0.094 and 0.076 in the case of constant water depth. In the varying depth, the parameter, h/L, are 0.197~0.052 and 0.153~0.043. From numerical results shown, the wave heights would decrease about 20% after passing through 180m gravel seabed which is formed by λ=0.442 and kp=2.23×10-7m2 gravel. It is also shown that applying the intrinsic permeability and porosity to simulate the gravel seabed is quietly reasonable in this research.

並列關鍵字

Gravel seabed ； Boussinesq ； Intrinsic permeability

參考文獻

24.林銘崇、丁肇隆、張國緯(2002)「應用Boussinesq方程式在一維波浪場上之數值計算」，海洋工程學刊，第2卷，第1期，15頁-31頁。

27.林銘崇、丁肇隆、張宇、許朝敏(2006)「波浪通過透水介質之變形」，第二十八屆海洋工程研討會論文集，343頁-348頁。

29.許朝敏(2004)「波流場中波浪變形之研究」，博士論文，國立台灣大學。

2.Chang, H.H. (2004) “Interaction of Water Wave and Submerged Permeable Offshore Structures,” Ph. D. Thesis, National Cheng Kung University, Tainan, Taiwan.

3.Cruz, E.C., Isobe, M. and Watanabe, A. (1997) “Boussinesq Equations for Wave Transformation on Porous Beds,” Coastal Eng., Vol. 30, pp.125-156.