沒水板對非線性波溯上消減研究

Abstract

本文以邊界元素法(Boundary Element method, BEM) 模擬直推式數值水槽，並於數值水槽置入沒水板，研究沒水板消減有限振幅波溯上的效果。數值模式包括消除造波板引起之二階自由波、測試水槽末端加入海綿層及輻射邊界消減反射波之效果，並以Euler-Lagrangian混合模式及二階Taylor級數展開法追蹤自由水面水粒子的運動軌跡，為了增加數值計算精確度，各種物理量之切線方向一階及二階的微分都使用Cubic Spline求得。首先發展出非線性波數值水槽並與Stokes五階解比較，利用數值水槽計算非線性波浪溯上高度並與實驗值比較驗證本文數值模式之正確性。於數值水槽加入沒水板探討沒水板對波浪溯上的影響，發現波浪的溯上與沒水深度、沒水板與堤腳的距離、沒水板傾角、沒水板的寬度、及傾斜堤面之坡度有關。透過沒水板的波浪與堤面反射的波浪之相位差的不同，會產生不同的駐波波高，發現在愈大的駐波波高會有愈大的溯上高度，因此影響因子可綜合成穩定後的駐波波高。大致上，加入沒水板後均能降低溯上高度，而相對溯上高度隨著相對水深kh增加而有週期性遞減的趨勢，尖鋭度愈大相對溯上高度則愈低。

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 and velocity vector are computed and compared with the fifth order Stokes wave theory. The numerical scheme is also applied to study the runup of nonbreaking waves on plane beaches. The maximum runup predicted by this study is compared to labotary data from other investigations and it is demonstrated that it models the runup process adequately. After having verified the accuracy of the numerical scheme, the effects of submerged plate on the runup of nonbreaking waves are investigated in detail. Our numerical results show that runup is affected by the submerged depth, the width, the inclined slope of plate, and the clearance between plate and beach. But the resulting factors can be intergrated by a variable of partial standing wave height between submerged plate and beach. Runup height increased as well as partial standing wave height increased. Generally, the runup height tends to reduce when a submerged plate is set in the wave tank. The relative runup height periodically decreases as the relative water depth increases; the relative runup height decreases as the wave steepness increases.