本文旨發展二維數值黏性造波水槽，用以模擬波浪通過潛堤之流場變化。為模擬真實流體的運動情形，本模式擬求解非穩態雷諾平均方程式 (RANS) 與紊流模式 ( model)，並採用質點等位函數法追蹤波浪碎波時複雜自由液面的變化情形。數值水槽上游設置一平板式造波機產生入射波。本模式利用有限解析法離散控制方程式，同時配合SIMPLER加速疊代方法耦合速度與壓力的計算。等位函數計算乃採用四階TVD Runge-Kutta method與五階WENO scheme求解之。其準確度經由數值實驗測試 (Zalesak’s problem)，結果令人滿意。
本文內容包含兩大主題，第一部份介紹一新的入反射分離方法，用以探討週期波通過潛沒防波堤時，在未碎波的前提下，波浪流場的高階成分波及其能量傳遞關係。為分析週期波通過潛堤時，雜亂波形的演變機制，本研究利用四支(或四支以上)波高計分離高階入反射成分波，包括自由波 (free modes) 與強制波 (locked modes) 等。本方法利用傅利葉轉換 (Fourier transform) 分離複合波中各階倍頻波，再應用最小二乘法 (the least squares method) 降低實驗量測誤差以求得各階振幅。為避免計算時數值發散的問題，波高計擺放位置亦建議於文中。本方法之準確性及其敏感度，經由人為給定時序列資料或加入人工雜訊測試，獲得不錯的成果。在實際應用方面，本文擷取波高計於防波堤上下游量測所得波浪時序列資料，經過分析並與過去研究 Goda and Suzuki (1976) 和 Mansard and Funke (1980) 比對，印證本方法可析出完整的高階入反射成分波，有別於過去研究僅可析出自由波的假設。

第二部份：當波浪碎波時，流場運動機制變得複雜且難以量測。為探討碎波流場機制，本文應用數值模式模擬波浪通過潛沒防波堤時碎波之流場特性及其自由液面的變化。本模式模擬孤立波於半無限長潛堤上碎波之數值結果與 Yasuda et al. (1997) 實驗量測所得結果吻合，驗證本模式可適切地描述碎波波型變化。為了解碎波時能量的損失情形，本文經由變換不同尺度的防波堤，討論波浪發生前後包括淺化，水體重合與飛濺時，能量於動能及位能之間的轉換情形。數值結果顯示能量損失於水體重合時有明顯增加的趨勢。此外，隨著潛堤高度的增加，碎波發生位置由潛堤下游往前移至潛堤上方，而碎波型態則由溢波 (spilling breaker) 逐漸演變成捲波 (plunging breaker) 乃至崩波 (collapsing breaker) 型態。

In present study a two-dimensional numerical wave tank in viscous fluid was developed and applied to simulate the propagation of water waves over a submerged breakwater. The unsteady, two-dimensional Reynolds Averaged Navier-Stokes (RANS) equations and the turbulence model ( model) were solved for simulating the realistic fluid. A hybrid particle level set method was adopted to capture the evolution of the highly complex free surface. A piston-type wavemaker was also set up in the computational domain to produce the desired incident waves. In this model the governing equations were discretized by means of a finite-analytical scheme. The SIMPLER algorithm was used to calculate the coupled velocity and pressure fields. The evolution of level set method was solved using forth-order TVD Runge-Kutta method and fifth-order WENO scheme, and the accuracy was confirmed by solving the Zalesak’s problem.
Two major subjects were discussed in present study. First, to understand the characteristics of the complicated wave fields as a periodic wave train propagated over a submerged breakwater without breaking, present research proposed a new technique to separate incident and reflected higher harmonic waves using four or more spatially separated probes. Both the free and locked modes in the higher harmonics of the regular waves can be isolated. The complex waves are decomposed into individual frequency components using the Fourier transform. The least squares method is applied to minimize the error caused by possible signal noise and to obtain the equations for solving the unknown parameters related to the wave amplitudes. Probe spacing condition for preventing singularity in the calculation is provided. The accuracy of this method is verified by applying it to resolve artificial waves with arbitrarily selected amplitudes. The sensitivity of this method to the noise inevitably associated with the experiments is also tested. The free surface elevation data collected from probes located upstream and downstream of a submerged breakwater in a numerical wave tank are analyzed to demonstrate the applicability of this method. The results are compared with those obtained using the methods of Goda and Suzuki (1976) and Mansard and Funke (1980). The comparison indicated that this method gives exactly the same first harmonic incident and reflected wave amplitudes as the other two methods. The full modes in the higher harmonics can be determined using this method, while the higher harmonics are presumed to be free waves in the other two methods.
Second, as the wave breaking, the internal kinetics of fluid flow became complicate and was difficult to measure in laboratory. In order to investigate the kinematics properties of overturning waves, present numerical model was performed to simulate the internal velocity and its corresponding surface evolution as the water wave passed over the submerged breakwater. The evolution of a solitary wave overturning on a submerged breakwater was in good agreement with the experimental data of Yasuda et al. (1997). According to the numerical results, the maximum flow velocity increased gradually during the wave breaking process until the third times of reattachment occurred. To realize the energy loss during wave breaking, the energy translation between kinetic energy and potential energy was discussed systematically with difference scales of submerged breakwater at several significant stages including the shoaling process, re-attachment and splash-up stages. The numerical results showed that the energy loss increased intensively at the stage of re-attachment. Besides, the location of the breaking point moves from the downstream of the breakwater to be above the breakwater, as the breakwater height increases; and the wave breaking type changes from the spilling breaker to plunging breaker and then collapsing breaker.

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