本研究提出一種新的簡單方法，用於計算波浪邊界層中流體-固體交界面之床面滑移速度。根據已知實驗和數值模擬結果，當波浪通過剛性透水底床時，在流-固交界面上存在一個非零的滑移速度。由往昔的眾多研究，所預估之底床滑移速度均偏小。在波浪與剛性透水底床之邊界值問題中，滑移現象取決於底床的性質。滑移速度邊界條件(SVBC)通常是用於解釋流體在多孔介質的滑移現象。傳統的SVBC或滑移速度只考慮在單向流之流況，然SVBC在簡諧運動中的應用仍然是一個懸而未決的問題，在實際之案例中，必須尋求一個簡單的公式用以評估波浪邊界層之底床滑移速度。
本文第一部份，利用史托克斯第二類問題和滑移長度模式(SLM)導出一個新的滑移速度和滑移係數。海床的滲透性和粗糙度被選擇作為滑移特性長度。解析結果顯示滑移速度取決於波浪週期和壓力梯度；而波浪雷諾數、沉積物滲透性及底床粗糙度則會影響滑移係數。理論得到的滑移速度與實驗結果具有良好的一致性。
延伸滑移係數之理論來估算在層流/紊流粗糙床面中床面剪應力是本研究的第二部分。根據滑移係數公式，可以推導出波浪摩擦係數與滑移係數之簡單關係，在不同的流況中可估算出波浪通過多孔介質床面之摩擦係數。本研究之理論公式顯示波浪摩擦係數與相對床面粗糙度A/ks成反比，當已知波浪條件及沉積物參數時，該公式可以很方便地定出波浪摩擦係數，而無需利用特定的實驗所推導出的回歸公式。本文另外在實驗室直接量測在多孔床面由波浪所引起之剪應力，並檢核理論之適足性。
　　在層流區，與已知之試驗結果對照後，顯示本文理論計算結果具有良好的一致性。在紊流-粗糙區中，本研究考慮渦流粘滯係數的影響，並採用零方程模型用於估計平均渦流粘滯係數。所得波浪摩擦係數理論之預估值是相當接近於實驗量測結果，其結果優於其他現有的回歸公式。在小粗糙度區域中，本研究所提出之公式仍可用來計算該區間之波摩擦係數；因此，滑移係數理論可擴展至紊流-粗糙區之波浪摩擦係數之預估上。實驗結果進一步顯示，在多孔介質中的波浪摩擦係數會受沉積物滲透性的影響。根據與往昔結果驗證後顯示，本研究所提供之方法，可以應用在實際情況下估算床面滑移速度和床面剪應力及提供工程規劃及數值模擬參數設定或計算之參考。

In the present study, a new and simple method for determining the slip velocity (also called the bed velocity) on the solid-fluid interface in the wave boundary layer is proposed. Based on experimental and numerical results, when waves travel over a rigid permeable seabed, a nonzero slip velocity exists at the solid-fluid interface. The defect of a small slip velocity has been found to occur in previous studies and is usually encountered in fluid-porous layer problems. In the wave-rigid permeable seabed problem, the slip effect depends on the properties of the seabed. The slip velocity boundary condition (SVBC) is one specification of the slip conditions and is usually applied to explain the slip phenomenon in a fluid-porous layer problem. However, the traditional SVBC or the slip velocity is only considered in a single flow, and the application of SVBC in harmonic motion is still an open problem that necessitates a simple formula for determining the slip velocity in realistic cases.
The Stokes’ second problem and the slip length model (SLM) are applied to derive a new slip velocity and a slip factor in this paper. Both the permeability and the roughness of the seabed are chosen as the characteristic length of slip motion. The analytical solution shows that the new slip velocity depends on the wave period and the pressure gradient, and the slip factor is related to the wave Reynolds number, the permeability, and the roughness of the seabed. The resultant slip velocity shows good agreement with the experimental results.
Using the slip factor to determine the bed shear stress in the laminar/turbulent-rough regimes is the second part in this study. A simple relationship is developed to theoretically estimate the wave friction factor in various flow regimes in the porous media based on the slip factor formula. The theoretical formula shows that the wave friction factor varies inversely with the relative bed roughness,A/ks , over a rough bed and that it can be conveniently determined if wave conditions and sediment parameters are known without using a specific regression formula deduced from experiments. A laboratory experiment that directly measures the wave-driven bed shear stress dominant in the turbulent regime with a permeable bed is used to examine the newly-derived relationship.
In the laminar regime, the comparison demonstrates that the theoretical results determined by the proposed formula are in good agreement with existing measurements. In the turbulent-rough regime, the influence of eddy viscosity is considered in the present model and the zero-equation model is used to estimate an average eddy viscosity. The theoretical wave friction factor is reasonably close to the experimental measurement, and considerably better than that obtained by other existing regressions. It is also found that the wave friction factor in the small zone can be described by the present model, with comparisons showing that the slip factor theory can be extended to estimate the wave friction factor in the turbulent-rough regime. Additionally, the proposed relationship is demonstrated to be effectively used in an alternate rough bed. Experimental results further indicate that the wave friction factor in porous medium is affected by the permeability of the sediment. Based on many comparisons with previous results, it is concluded that the method provided by the present study can be applied for determining the slip velocity and bed shear stress and setting up the parameter in the real case and numerical model.

誌謝....................................................................................................................................i
中英文摘要.......................................................................................................................ii
目錄..................................................................................................................................vi
圖目錄.......................................................................................................................................................ix
表目錄.....................................................................................................................................................xiii
符號表............................................................................................................................xiv
第一章 緒 論
1.1前言..............................................................................................................................1
1.2前人研究及文獻回顧..................................................................................................2
1.2.1底床滑移速度量測與評估.............................................................................2
1.2.2底床剪應力量測與評估.................................................................................3
1.3研究動機及目的..........................................................................................................5
1.4研究方法......................................................................................................................6
1.5本文架構......................................................................................................................7
第二章 滑移模型之理論及應用
2.1流固交界面之滑移現象..............................................................................................9
2.2滑移速度邊界條件-滑移長度模式..........................................................................12
2.3滑移邊界條件於水動力問題之應用........................................................................15
2.3.1 Beavers及Joseph (1967)滑移速度邊界條件..............................................15
2.3.2 Saffman滑移速度邊界條件於波浪問題之應用........................................16
第三章 波浪與多孔介質交界面之滑移速度
3.1邊界條件之修正及設定............................................................................................19
3.1.1上部邊界條件...............................................................................................19
3.1.2沉積物粒徑與等值粗糙度...........................................................................19
3.1.3波浪與多孔介質交界面之邊界條件...........................................................21
3.2基本假設與理論分析................................................................................................23
3.3滑移速度及滑移係數................................................................................................26
3.3.1流體加速度效應...........................................................................................26
3.3.2壓力梯度效應...............................................................................................27
3.3.3經驗常數 之決定......................................................................................28
3.4利用Saffman(1971)之滑移速度邊界條件所得出之理論解..................................30
3.5理論之驗證................................................................................................................30
3.5.1與李(1994)及Lee et al.(1996)試驗之比較..................................................30
3.5.2與Liu et al.(1996)試驗之比較.....................................................................36
3.5.3與(3.30)式之比較.........................................................................................39
3.6誤差原因及分析........................................................................................................40
3.7敏感度分析................................................................................................................42
3.7.1波浪雷諾數對滑移係數及滑移速度之影響...............................................42
3.7.2底床粗糙度及滲透係數對滑移係數之影響...............................................45
第四章 底床剪應力之評估與水工模型試驗
4.1滑移係數與底床摩擦係數之關係............................................................................54
4.2紊流區渦漩黏致係數之評估....................................................................................55
4.3底床剪應力之試驗及剪力計之製作........................................................................57
4.3.1底床剪應力之試驗設施...............................................................................57
4.3.2底床剪應力估算方式...................................................................................59
4.3.3量測原理.......................................................................................................65
4.3.4剪力計之構造及細部設計...........................................................................66
4.3.5率定及水中動力分析...................................................................................71
4.3.6精度分析.......................................................................................................73
4.4水工模型試驗設備及配置........................................................................................75
4.4.1造波斷面水槽...............................................................................................75
4.4.2多孔介質底床之鋪設及剪力計安裝...........................................................76
4.4.3試驗條件與試驗流程...................................................................................79
4.5分析方法....................................................................................................................81
4.6試驗結果....................................................................................................................82
4.6.1試驗結果之可靠度分析...............................................................................82
4.6.2水平總力.......................................................................................................85
4.7理論與試驗結果之比較............................................................................................88
4.7.1層流區-與You and Yin(2007)試驗之驗證..................................................91
4.7.2紊流-粗糙區(Turbulent-rough regime)-與本次試驗結果之比較...............91
4.7.3渦漩黏滯係數之驗證-與Mirfenderesk and Young(2003)試驗與其他
理論公式之驗證..........................................................................................93
第五章 特性分析與討論
5.1本模式之等值粗糙度評估..............................................................................95
5.2剪力與自由水面之相位偏移..........................................................................96
5.3理論公式在層流區及紊流-粗糙區之應用....................................................98
5.4最佳渦漩黏滯係數之評估............................................................................103
5.5滲透係數及多孔界面對剪應力之影響........................................................105
5.6由剪力計長度所引起之誤差........................................................................107
5.7底床穩定性之應用........................................................................................108
5.8能量損耗及波浪衰減係數............................................................................110
第六章 結論與建議
6.1結論..........................................................................................................................115
6.2建議..........................................................................................................................117
參考文獻.......................................................................................................................119
附錄A............................................................................................................................129
附錄B............................................................................................................................131
附錄C............................................................................................................................133
簡歷...............................................................................................................................135

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