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Title: | 波浪通過透水介質之變形 Wave Transformations over Porous Media |
Authors: | Yu Chang 張宇 |
Advisor: | 林銘崇 |
Co-Advisor: | 丁肇隆 |
Keyword: | 布斯尼斯克方程式,透水介質,孔隙率, boussinesq equation,porous media,porosity, |
Publication Year : | 2006 |
Degree: | 碩士 |
Abstract: | 摘要
本文旨在探討孔隙介質對波浪變形的影響,理論模式方面參考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,本模式的適用性相當良好。另外,考慮不同孔隙率(0.0、0.1、0.2、0.3、0.44)及不同滲透性係數(kp=2.5×10-8m2、2.5×10-7 m2)之透水底床,在不同波浪條件下,對波浪變形之影響;由主頻波及二、三階諧和波在空間上之變化情形可知,在孔隙率小於0.44的條件下(kp=2.5×10-8 m2),對波浪衰減影響程度大致是隨著相對水深增加而變大,當相對水深介於0.293至0.489間,計算結果顯示孔隙率愈大,波浪衰減愈顯著。但相對水深小於0.2時,孔隙率與入射波浪週期的變化並沒有清楚的規則性存在,原因應該是相對水深太淺時,此方程式對於波浪通過透水介質的模擬較無法準確。而在滲透性係數kp=2.5×10-7 m2時,在不同波浪條件下,波浪衰減情形並不是隨著孔隙率之增加而增加,而是孔隙率須大至某一值後,增加孔隙率才可增加波能的衰減。 ABSTRACT The purpose of this research is to investigate wave deformation passing through different submerged porous obstacles. 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, and it introduces a parameter related with shoaling and seabed contour, Madsen and Sørensen (1991), to apply to the situation a larger 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 previous research. After examining the effect upon the porosities and the intrinsic permeability ,kp under different wave conditions, the deformation of the primary wave, second order harmonic wave and third order harmonic wave indicates that the wave height decreases as the relative depth increases when the condition of the porosity is less than 0.44 and kp=2.5×10-8m2. The wave height decreases significantly along with the larger porosity when the relative depth is between 0.293 and 0.489. But the phenomenon of the wave height decrease for the various porosities is not so regular when the relative depth is less than 0.2. The reason of the above situation is the larger non-linear effect at the shallow water condition; therefore the simulation of the wave passing through a porous obstacle is not suitable. When kp=2.5×10-7m2, the wave height does not decrease simply with the increase of the porosity; rather the porosity must be greater than a specific value in order to achieve a greater wave energy decay. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/31628 |
Fulltext Rights: | 有償授權 |
Appears in Collections: | 工程科學及海洋工程學系 |
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