臺灣博碩士論文加值系統

觀察波浪表面發現存在沿流向之條痕結構，其結構與牆面紊流邊界層（wall turbulent boundary）相似，為探討其結構特性及其成因，故本研究應用前人於牆面紊流邊界層之研究方法，分析未破碎波浪之自由液面的數值模擬資料，發現低溫條痕之分布與沿流向高速條痕之分布相似，故為低溫高速條痕。透過沿流向平均發現條痕亦與渦度擾動有關，進而以渦度方向角度、渦旋結構辨識、條件平均法分析水面下之紊流流場，發現其具有成對沿流向之相關紊流結構（coherent turbulent structure），且其為反向旋轉，而該結構多分布於波背處，而隨時間發展逐漸朝沿流向延伸。針對上述之特性，可以透過渦度傳輸方程式說明，於波背處之沿流向渦度逐漸增大，於波前處逐漸減小，而其整體效應為隨時間逐漸增大，故使紊流結構朝沿流向延伸。比對Craik與Leibovich提出之理論，進行穩定性分析，其結果發現與數值模擬資料之流場吻合，故流場中成對沿流向之相關紊流結構即為朗繆爾環流（Langmuir circulation），並造成條痕結構。

Streaky structures along the streamwise direction can be observed on the wavy surface, and they are similar to what is found in the wall turbulent boundary layer. To study the properties of these structures, the research methods used in the wall turbulent boundary are applied to the analysis of the simulation data of the non-breaking surface wave in this thesis. It is found that the distribution of high-temperature resembles the distribution low-speed streaks, and are so called high-temperature low-speed streaks. By using streamwise averaging, it is found that the streaks also correlate closely with fluctuation vorticity. Further, the methods of vorticity inclination angle, vortex identification and condional averaging are used to analyze the underwater turbulent flow field, and show that there exist pairs of the streamwise coherent turbulent structures which are counter roation. The most of them are lain in the wave back and stretched along the streamwise over time. On the above properties, they can be illustrated with vorticity transprot equations. The streamwise vorticity grows gradually in the wave back, and decaies in the wave front. Then, the total effect is positive, and the streamwise vorticity is strected over time. Comparing with the theory which Craik and Leibovich proposed, and executing the stability analysis, the charterisitcs of simulation data fits in with the results of the stability analysis. It confirms that the pairs of the streamwise coherent turbulent structures are Langmuir circulations which lead to streaky structures.

致謝 i
中文摘要 ii
Abstract iii
目錄 iv
圖目錄 vi
表目錄 xxx
第一章、 前言 1
1.1 研究背景 1
1.2 數值模擬數據之產生 3
1.3 論文架構 6
第二章、 流場結構分析 7
2.1 渦度剖面圖 44
2.2 相位平均 48
2.3 沿流向平均 67
2.4 渦度方向角度 105
2.5 渦旋結構辨識 126
2.5.1 速度梯度張量之第二不變量 (The second invariant of ∇u) 127
2.5.2 速度梯度張量之複數特徵值 (The complex eigenvalues of ∇u) 129
2.5.3 S2+Ω2 之第二特徵值 (The second eigenvalues λ2 of S2+Ω2) 131
2.5.4 速度梯度張量之複數根之虛數部分─渦流強度 (The image part σci of the complex eigenvalues of ∇u, swirling strength) 133
2.5.5 辨識結果 134
2.6 條件平均法 (conditional averaging methods) 172
2.7 渦度傳輸方程式 (Vorticity transport equations) 188
第三章、 流場穩定性分析 211
3.1 理論介紹 211
3.2 結果與討論 217
第四章、 結論 222
參考文獻 224
附錄一 相平面法 226
附錄二 契比雪夫多項式 232

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