在無滑移邊界紊流邊界層中，學者之研究證實存在具有組織的條痕結構，無 因次化後的平均條痕間距趨於一定值 𝜆̅̅̅ ≅ 100，且低速條痕之間距分佈近似於對+ 數常態分佈［Smith and Metzler (1983)］。在風驅動自由液面紊流邊界層中亦明顯地 觀察到相似的條痕結構，經學者們的研究發現，由於水面紊流邊界層中存在成對 試驗為 cool-skin case。本研究利用數位影像處理之技術，包含：二維整體經驗模 態分解法、拉普拉斯金字塔法和高斯低通濾波法，透過此三種不同雜訊去除的方
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不論是 Aeolotron 2014 或是 Aeolotron 2012 之試驗資料，以不同方法將影 像進行平滑化後，其分析結果顯示整體趨勢相同：隨著摩擦速度的增大，有因次 之平均條痕間距減小，無因次之平均條痕間距增大。
有因次之平均條痕間距隨摩擦速度遞增而減少，Melville et al. (1998) 將追跡 質點灑入水面，觀察不同風速驅動流場，水面紊流邊界層之結構，其追跡質點會 逐漸匯聚在高流速區域，形成高速條痕，試驗風速分別以 3 m/s、4 m/s 和 5 m/s 驅動流場，其所對應之條痕間距分別 ~7 cm、~5 cm 和 ~3 cm（如圖 5. 2 所 示），隨著試驗風速愈大，水面條痕結構愈緊密，條痕間距愈減小，與本研究所得 結論相同。
無因次平均條痕間距是隨著摩擦速度遞增而增加，與前人研究牆面紊流邊界 層無因次平均條痕間距 𝜆̅̅̅ ≅ 100 之結論不相同，本研究結果顯示：風剪驅動水+ 面紊流邊界層之無因次平均條痕間距非一定值，且似乎有隨摩擦速度增加而線性 遞增之趨勢。統計得到條痕間距分佈之後，參考 Ryanzhin et al. (2005) 考慮指數分 佈、伽瑪分佈、對數常態分佈、馬克士威分佈、雷利分佈、韋伯分佈，以多種理 論分佈對條痕間距分佈進行最小平方擬合，再透過卡方適合度檢定判斷其統計特 性。結果顯示低溫條痕之間距分佈近似於對數常態分佈，與無滑移邊界之紊流邊 界層的條痕分佈特性相同。
盼此分析風浪表面熱圖像的條痕結構之統計特性，提供後人研究風剪驅動自 由滑移邊界紊流邊界層的結構之參考資料。
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表 5. 1、Schnieders et al. (2013) 分析 Aeolotron 2012 數據之結果
表 5. 2、古孟巧 (2015) 分析 Aeolotron 2012 數據之結果 𝐀𝐞𝐨𝐥𝐨𝐭𝐫𝐨𝐧 𝟐𝟎𝟏𝟐, 𝐊𝐮
摩擦速度 𝑢∗ [cm/s] 平均間距 𝜆̅ [cm] 平均間距 𝜆̅̅̅ +
0.2 1.634 32.678
0.29 1.410 40.903
0.47 1.298 61.016
0.76 1.156 87.846
1.3 1.062 138.026
𝐀𝐞𝐨𝐥𝐨𝐭𝐫𝐨𝐧 𝟐𝟎𝟏𝟐, 𝐒𝐜𝐡𝐧𝐢𝐞𝐝𝐞𝐫𝐬
摩擦速度 𝑢∗ [cm/s] 平均間距 𝜆̅ [cm] 平均間距 𝜆̅̅̅ +
0.2 1.3 26
0.29 1.09 31.61
0.47 0.81 38.07
0.76 0.59 44.84
1.3 0.87 113.10
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(𝑎)
(𝑏)
圖 5. 1、平均條痕間距與摩擦速度之關係圖。橫軸為摩擦速度，單位以 cm/s 表 示；縱軸為平均條痕間距，圖 (𝑎) 單位以 cm 表示，圖 (𝑏) 單位以無因次表示；
虛線為無滑移邊界紊流邊界層之理論無因次平均條痕間距值 𝜆̅̅̅ = 100。黑色圓形、+ 方形和菱形，分別代表利用二維整體經驗模態分解法、拉普拉斯金字塔法和高斯 低通濾波法，將 Aeolotron 2014 影像平滑化，並分析平均條痕間距之結果。紅色 正三角形和藍色倒三角形分別代表 Schnieders et al. (2013) 和古孟巧 (2015) 分析 Aeolotron 2012 影像之結果。
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圖 5. 2、條痕間距與風速之關係圖。橫軸為風速，單位以 m/s 表示；縱軸之單位 以 cm 表示。黑色圓形、倒三角形、正方形，分別表示水面條痕間距（surface streak spacing）、剪力層深度（shear layer depth）、水面波長（surface wavelength）。【原圖 來源：Melville et al. (1998)】
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附錄一、卡方分佈臨界值表
【原表來源：Thompson (1941)】
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附錄一、卡方分佈臨界值表（續）
【原表來源：Thompson (1941)】