非線性波與透水潛堤的交互作用

Abstract

本文以邊界元素法(BEM)發展出一直推式非線性波之數值造波水槽，在水平底床置入一透水矩形潛堤，以有限差分法(FDM)來模擬潛堤內流體的運動，並於水槽末端加入一假想海綿來吸收入射波。模式中以Euler-Largrangian來描述自由水面的運動，使用曲線近似法(Cubic Spline)求得水面點各種物理量之切線方向一階和二階的微分值，再利用Taylor級數展開法求得下一時刻的水位資料；此外，在潛堤內利用有限差分法（壓力修正法）配合交錯網格系統來求得潛堤交界處下一時刻所需的邊界數值。模式中亦使用了合適條件(Compatibility Condition)及平滑技巧(Smoothing Technique)來增加模式的穩定性，藉以瞭解非線性波與透水潛堤間的交互作用。 在本文研究中，給定一相同尺寸的潛堤，以改變入射波的條件來探討波浪對透過係數的影響。首先數值結果與驗證之實驗數值結果比較，雖然在某些方面有些差異性，但是趨勢是很相似的，因此證明本數值模式的正確性。在最後的結果發現，波浪尖銳度越大者，則透射率就越小，在相對水深kh=1.0-2.0間皆可明顯的觀察到；由結果也可觀察到在相同的波浪尖銳度下，相對水深越大者，則透射率就越大，因此可得此透水潛堤對於波浪尖銳度大且相對水深小者有較良好的消波效果。

Based on the boundary element method, a numerical model for the simulation of nonlinear wavefields generated by a piston-type wavemaker has been developed. A spongy layer is set in front of the wall at the end of the tank to absorb the incoming wave energy. In the present model, a time-steping largrangian technique is employed to track the free surface movement. The associated velocity of the free surface are computed by second order numerical integrated in time. The finite difference method and a staggered grid are applied to computing boundary values of the submerged porous breakwater. The compatibility condition and the smoothing technique are applied to increasing the stability of the numerical model. In this study, the numerical model is applied to study the deformation of nonlinear wave propagation over a submerged porous breakwater. The accuracy of the present numerical model is proved by comparing results of the present numerical model and the laboratory experiment. FFT is applied to detect the wave energy of harmonic components in different locations of the numerical tank. The numerical results show that the fully nonlinear analysis is much different to the linear analysis, which proves the important of fully nonlinear analysis. According to the comparison of the numerical results, the transmission coefficient decreases as the wave steepness increases at the same water depth. The results also show that the transmission coefficient increases as the water depth decreases. For this reason, the energy loss rate is better when the wave steepness is higher and the water depth is lower. In addition, the results also show that the transmission coefficient is affected by the porosity. The transmission coefficient decreases as the porosity increases.