二階有限振幅波理論應用於造波問題及可透水防波堤問題之研究

Abstract

本文是以數值計算的方式；探討活塞式造波機與投入式造波機的二階有限振幅波之造波理論及探討二階有限振幅波與可透水防波堤之交互作用問題。其所採用的數值方法為線性元素的邊界元素法，並配合Vantorre (1986) 的複數運算技巧；將因複數運算所產生的二階與時間無關的分量加入考慮，以求得完整約二階有限振幅水波之問題。 於造波問題的研究中，第一階分量之線性波高與造波板衝程(stroke) 之比值以及第二階分量中的自由波 (free wave) 波高與Stokes波波高之比值均是隨著不同的波浪條件而變化。並且為了消除消散波之效應，文中是將轎射邊界放在距造波板2.0倍波長之位置上，並藉由計算區域內外之波形變化關係以驗證其適當性。同時為了明瞭二階有限振幅水波波形隨時間之變化關係，文中也將不同波浪條件下於不同位置上的波形繪出以窺其結果。又為了驗證本數值模式之正確性，除了將第一階線性波高與造波板衝程之比值以及第二階自由波波高與Stokes波波高之比值與其他學者的解析解以及實驗結果做一比較之外，也利用活塞式造波機所產生的二階波形結果與Madsen (1971) 的實驗結果做一比較，其比較的結果均顯示了本模式的正確性。 而在可透水防波堤問題之研究中，則是利用Sollitt and Cross (1972) 的多孔流速度勢能理論 (pore velocity potential theory) 探討因孔隙介質的變化、波浪條件之改變以及可透水結構體形 狀之變化對波浪變形所產生之影響，同時也為了明瞭數值模式之 正確性，不論是摩擦係數或者是反射係數以及透過係數，均與其 他學者之解析解以及實驗結果做一比較，而這些的比較結果均可 得到合理之印證。同時為了消除消散波的效應，文中也是將輻射 邊界的位置，放在距離結構體2.0倍波長的位置上，並藉由區域內 外之波形變化關係以說明其適切性。同樣地，利用不同波浪條件 在不同位置上的波形與時間之變化關係，來說明考慮二階有限振 幅水波理論後對波浪的影響。 而由此論文的討論結果可以發現，利用完整約二階有限振幅波理論於近海海域問題的模擬時，除了其結果明顯的比只使用線性理論的模擬結果來的適當之外；且其波浪的非線性特性也可藉由此模式的模擬結果得知。

Based on a two dimensional finite amplitude water wave theory, this study develops the boundary element method with linear element to examine the generation of waves by wavemakers (piston- type wavemaker and plunger-type wavemaker) and the fluid field of water wave interaction with a permeable breakwater. According to Vantorre (1986) discussions, two harmonic functions with the same frequency product include a time-independent term. The complete solution of the second order boundary value problem should involve the time-independent part. To generate waves by wavemakers, the ratio of the linear wave amplitude generated by wavemakers to the wavemaker stroke and the ratio of second harmonic free wave amplitude to Stokes wave amplitude are computed for different relative water depths. Herein, the radiation boundary is placed at two times wave length distance away from the wavemaker to eliminate the evanescent mode. The spatial evolution of the wave profiles presented in this study confirms that the distance is appropriate. In addition, the temporal evolution of the wave profiles is also presented for different distances. More- over, comparing the numerical results with previously published analytical and experimental ones confirms the numerical technique's accuracy. Furthermore, comparing the numerical wave profile evolution by a piston-type wavemaker with the experimental results of Madsen (1971) demonstrates a good correlation. In the study of permeable breakwater, the pore velocity potential theory of Sollitt and Cross (1972) as a basis for the work done. This study also computes the first order and the second order wave profiles, reflection and transmission coefficients and the amplitude ratio of the second order components. Material properties of the permeable breakwater, wave conditions and the types of the permeable breakwater heavily influence the friction coefficient, the reflection coefficient and the transmission coefficient. The accuracy of the second order solutions calculated from present numerical model has been proven to correlate well closely correspond to the analytical and experimental results obtained by most previous studies. To eliminate the evanescent mode, the radiation boundaries are also placed at two times wave length distance away from the permeable breakwater. In addition, the spatial evolution of the wave profiles is presented to confirm that the distance is adequate. Again, the temporal evolution of the wave profiles is also presented for different distances to express the effect of the second order finite amplitude water wave theory. According to that comparison, not only is the complete solution of the second order numerical scheme is better than the solution of the linear wave theory but the nonlinear effect can be simulated in shallow water.