非線性波浪通過傾斜穿入式防波板的變形研究

Abstract

本文以邊界元素法模擬直推式造波之非線性波浪數值水槽，除了消除造波板所造成的二階自由波，並配合輻射邊界條件，且於水槽末端設置海綿層吸收前進波，用以避免反射波造成分析上之困難。模式中以Eulerian-Lagrangian數值技巧來追蹤自由水面水粒子的非線性運動，並使用曲線近似法求得自由水面點各種物理量之切線方向的一階與二階微分值，再利用泰勒級數展開求得下一時刻的水位資料。本研究模式中同時使用合適條件(Compatibility conditions)和平滑技巧來增加模式的穩定性，進而在水槽中設置單一與兩穿入式防波板，利用數值方法探討非線性波與防波板之間的交互作用，並將數值結果與實驗值比較驗證。驗證結果顯示本模式計算之非線性波結果與實驗結果有相同的趨勢，但由於本研究並未考慮現實的流體具有黏滯性與實際上的底床和防波板皆存在摩擦效應此兩個因素，所以本模式求得之透射率結果較實驗值略大。數值結果發現防波板的寬度、沒水深度、傾斜角度及兩防波板間距皆會影響波浪的透射率。大致上，入射波的相對水深愈大，波浪通過穿入式防波板的透射率則愈低；入射波的尖銳度愈大，對應的透射率亦愈低。增加防波板的沒水深度、增長防波板寬度及增加防波板的傾斜角度，均會降低透射率。相同條件之入射波通過兩防波板的透射率較通過單一防波板時為低，並在特定之兩板間距情況下，波浪在兩防波板之間產生共振，且對應著極高的透射率。

Based on the boundary element method (BEM), a time stepping lagrangian technique is developed to simulate the generation of nonlinear water wave by a piston type wavemaker in a numerical wave tank. The second order free wave which generated by wavemaker, due to finite displacement, is eliminated in this study. Besides radiation condition, a sponge layer is set in front of the end of the wave tank to reduce wave reflection. To demonstrate the accuracy of the proposed numerical scheme, the surface elevation is computed and compared with the fifth order Stokes wave theory. The numerical scheme is also applied to study the interaction of nonlinear waves with vertical thin barriers. The transmissivity predicted by this study is compared to laboratory data and numerical results from other investigations. After having verified the accuracy of the numerical scheme, the interaction of nonlinear waves with inclined thin barriers is investigated in detail. Our numerical results show that transmissivity is affected by the width, the submerged depth, the inclined slope of barrier, and the clearance between two barriers. Generally, the transmissivity decreases as the relative water depth increases; the transmissivity decreases as the wave steepness increases. Increasing the depth, the width and the inclined slope of barrier decrease the transmissivity. The numerical results indicate that the multiple barriers become more efficient than one barrier. Resonance occurs at a certain clearance between two barriers at which transmissivity becomes extreme.