內波是發生在密度分層流體中一種波動現象，本研究為了更了解連續內波傳
遞的特性，在水槽中做了一系列的實驗，總水深為45 公分。上層為厚10 公分的
淡水，下層為厚35 公分的鹽水，內波週期分別為2.5、5.5、6.6s，並利用Micro
ADV 量測剖面流速分佈。且利用超音波波高計、表面波波高計分別偵測內波、表
面波的波形。研究結果顯示，在密度分層界面的上方和下方粒子流速方向相反，
在界面附近的u 和w 流速分量最大，離開界面越遠則流速越小。當兩層水體密度
差變小時，流速會較小，導致內波能量變小。利用HHT 時頻分析來得知週期，並
與EMD 來互相比較。得知波形和流速週期一致，進而利用EMD 來探討理論-實驗
的差異性
當連續內波傳遞到斜坡時，可發現淺化開始發生，內波波形逐漸抬升，波峰
變得尖銳，在更接近斜坡邊界時後半段波形變得比較陡直，造成流體剪應力不穩
及紊流，使水體內部翻轉，最後在斜坡上產生反射、破碎混合等現象。本研究探
討不同尖銳度的內波傳遞至不同坡度之斜坡時反射率的變化，當坡度非常平緩
時，反射係數小，當坡度漸增，反射係數漸增並接近定值。在無斜坡情況下，內
波傳遞過程產生的紊流很小，只有在上層內波交界面附近才會有比較明顯的擾
動。但加入斜坡後，內波所產生的紊流很明顯的增加，動能消散率ε變大。利用
慣性消散法、TKE 法和自相關方法分別估算ε和τ，自相關法算出的ε會較大，
但趨勢都是一致，較接近斜坡處的ε會比較遠處的大，斜坡角度越緩所產生的紊
流會更加明顯。

Internal waves occur in the interface between two layers of fluids with density
stratification. In order to better understand the characteristics of continuous internal
waves, a series of experiments were conducted in a laboratory tank. The upper and
lower layers are fresh water of 15 cm thick and salt water of 30 cm thick, respectively.
The periods of internal waves are 2.5, 5.5 and 6.6 sec. A micro-ADV is used to
measure velocity profiles. Wave profiles at the density interface and the free surface
are monitored respectively by an ultrasonic and capacitance wave gauges. Our results
indicate that particle velocities (u and w) above and below the density interface have
opposite directions. The speed is peaked near the density interface and it becomes
weaker further away from the interface. Empirical Mode Decomposition is used to
remove noise from the observed particle velocities, and the period is consistent with
those derived from the interface elevations. The observed particle velocities also
compare favorably with the theoretical results.
When internal waves propagate without the interference of a sloping bottom, the
turbulence induced is rather insignificant. The turbulence is more significant only near
the density interface. With the existence of a sloping bottom, the internal waves
gradually shoal and deform, the crest becomes sharp and steep, finally the waves
become unstable, break and overturn. In this study the effect of bottom slope and the
steepness of internal waves on the reflectivity of incoming waves are investigated.
The reflectivity is smaller with gentler slope, and it increases and reaches a constant
value with steeper slopes. The observed energy dissipation rateεis higher near the
slope. Three methods were used to estimate the energy dissipation rate and shear
stress; namely, the inertial dissipation, the TKE and auto-correlation method. Theε
estimated from the auto-correlation method is larger than that from the other two
methods, but their trend is similar. The energy dissipation rate is found to increase
with a gentler sloping bottom.

謝誌……………………………………………………………………………………i
中文摘要………………………………………………………………………………ii
英文摘要 …………………………………………………………………………… iii
目錄 ………………………………………………………………………………… iv
圖目錄 ……………………………………………………………………………… vi
表目錄 ……………………………………………………………………………… x
第一章、緒論…………………………………………………………………………1
1.1 前言…………………………………………………………………………1
1.2 前人研究……………………………………………………………………3
1.3 研究動機和目的……………………………………………………………5
第二章、實驗設計與方法……………………………………………………………6
2.1 實驗水槽設備和儀器………………………………………………………6
2.1.1 實驗水槽設備………………………………………………………6
2.1.2 觀測儀器與軟體 …………………………………………………7
2.2 實驗設計 …………………………………………………………………16
2.2.1 實驗條件…………………………………………………………16
2.2.2 實驗過程…………………………………………………………22
第三章、資料分析方法………………………………………………………………25
3.1 流速資料分析 ……………………………………………………………25
3.2 表面波、內波資料分析……………………………………………………25
3.3 HHT(Hilbert Huang Transform) and EMD﹙Empirical Mode
Decomposition﹚………………………………………………………… 26
3.4 理論公式解……………………………………………………………… 27
3.5 反射率和反射能量計算………………………………………………… 29
3.6 剪應力和消散率的估算方法……………………………………………30
3.6.1 TKE（turbulent kinetic energy）法 ………………………………30
3.6.2 慣性消散（inertial dissipation）法 ………………………………31
3.6.3 自相關(auto correlation)法 ……………………………………… 32
第四章、實驗結果與討論……………………………………………………………35
4.1 內波流速剖面及物理特性……………………………………………… 35
4.1.1 無斜坡 ……………………………………………………………35
4.1.2 有斜坡…………………………………………………………… 46
4.2 實驗-理論…………………………………………………………………48
4.3 power spectrum ……………………………………………………………57
4.4 反射率和反射能量計算 …………………………………………………71
4.5 turbulence …………………………………………………………………74
4.5.1 點平均法(Bin average) ………………………………………… 74
4.5.2 移動平均法(Moving average)……………………………………74
4.5.3 相位平均法(Phase average) ……………………………………75
4.6 消散率 (ε) …………………………………………………………… 82
4.6.1 慣性消散法 ………………………………………………………82
4.6.2 TKE ……………………………………………………………… 85
4.6.3 Auto correlation……………………………………………………87
第五章、結論…………………………………………………………………………92
參考文獻 ……………………………………………………………………………95
附錄一 慣性消散法公式……………………………………………………………99

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