內波在大洋中傳遞時所產生的各種現象對海上結構物的破壞、營養鹽的懸浮傳輸或軍事上海底聲納的干擾等各領域均有重大影響。但在大洋中的密躍層厚度並非如理論假設般薄薄一層，因此有必要研究不同密躍層厚度對內波傳遞的影響。
本研究於一座0.5×0.7×12公尺長的內波水槽中進行實驗，在總水深H=50 cm中以淡、鹽水依密度分層佈置兩層水體，探討孤立內波在平滑底床與單一障礙物的環境中，隨密躍層厚度漸增對其物理量所造成的影響。
實驗中主要控制變因為：內波水槽中上、下層水深比(H1/H2)、造波區位能差(η0)及重複造波而產生密躍層厚度的變化。為探究密躍層厚度對孤立內波各物理量之影響，密躍層厚度的判斷則依賴密度計量測垂直密度剖面，經繪圖後估算其厚度(B)。本實驗之無因次密躍層厚度(=B/H；B為密躍層厚度，H為實驗水體總水深)關係，其初始值大致介於0~0.1之間。
由實驗成果得知，下沉型孤立內波之振幅在不同造波區位能差條件下，隨密躍層厚度增加而減小：初始振幅與傳遞振幅之減少率皆在小位能差( η0=10)時比大位能差( η0=15)明顯，波速在大位能差產生之變化量比小位能差者明顯，初始波長與傳遞波長變化皆無明顯變化，又初始能量與傳遞能量之減少率皆在小位能差時比大位能差明顯。上舉型孤立內波之變化與下沉型相似，但其減少率之明顯程度卻不及下沉型孤立內波之變化。

Internal solitary waves (ISW) have been detected on the interface of a stratified water column in the ocean. It is believed that ISW could affect oil drilling operations, nutrient pumping, and acoustic signal obstruction. In the ocean, the thickness of a pycnocline is finite which differs with the theoretical assumption as being a thin layer. This thesis reports the effect of an ISW propagation in various pycnocline thicknesses.
Laboratory experiments were conducted in an internal wave flume (0.5×0.7×12m) at the National Sun Yat-sen University, Kaohsiung, Taiwan. ISW in depression or elevation type were generaled using a stratified two-layer fresh/brine water system with a total depth of 50 cm in the flume. Upon creating an ISW propagating on a flat bed or over a triangular obstacle later, several physical parameters of the ISW (i.e. wave amplitude, phase speed, characteristic wave length, and wave energy) were measured or calculated for different thicknesses of the pycnocline.
The major controlling factors in the experiments included the depth ratio of the upper to lower layer H1/H2, interface displacement η0 between the wave generating chamber and the main flume, and the thickness of the pycnocline. The thickness of the pycnocline was estimated from the result of density profile in the vertical direction in the flume, experiments under the same H1/H2 and η was terminated when the pycnocline thickness became large enough.
As the thickness of the pycnoline increased, the values of all the physical parameters (including wave amplitude, phase speed, and wave energy) under consideration decreased. Their reduction rates were more significant in the case of small interface displacement (η0=10cm) than that with large η0=15cm. On the other hand, the changes in the physical variables associated with a depression ISW were more significant than those in an elevation ISW.

謝誌 I
中文摘要 II
Abstract III
目錄 IV
符號表 VII
圖目錄 VIII
表目錄 XIII
第一章 緒論 1
1.1 前言 1
1.2 文獻回顧 6
1.2.1 現場調查研究 6
1.2.2 實驗室研究 9
1.3 研究目的 11
1.4 本文架構 12
第二章 內波基本理論 13
2.1 前言 13
2.2 內波的生成、傳遞和減衰 14
2.2.1 內波的生成 15
2.2.2 內波的傳遞 15
2.2.3 內波的減衰 16
2.3 內波的型態與流場 17
2.3.1 內波的型態 17
2.3.2 內波的流場 19
2.4 影響密躍層厚度變化的機制 21
第三章 實驗室佈置 22
3.1 實驗設備與儀器佈置 22
3.2 實驗步驟與流程 26
3.2.1 實驗儀器之佈置 30
3.2.1.1 光滑水平底床(無障礙物) 30
3.2.1.2 單一障礙物 31
3.3 實驗設計 32
3.3.1 內波的生成 32
3.3.2 障礙物種類 34
3.3.3 重複造波次數的決定 35
3.4 實驗項目統計 35
第四章 實驗結果分析 41
4.1 實驗量測方法 41
4.1.1 儀器率定 41
4.1.2 資料的處理 43
4.1.3 濾波 43
4.2 孤立內波物理參數 45
4.2.1 振幅(wave amplitude, a) 45
4.2.2 孤立內波波速(phase speed, C) 45
4.2.3 特徵波長(characteristic wave length, Lw) 45
4.2.4 內波能量(wave energy, E) 47
4.3 實驗數據成果一覽表 48
4.4 實驗水體密躍層密度剖面 59
4.4.1 密躍層密度剖面 59
4.4.2 實驗密躍層厚度的展示 66
4.4.3 造波次數與無因次密躍層厚度的關係 72
第五章 孤立內波的物理特性 74
5.1 實驗室內波與波形理論的分析 74
5.1.1 孤立內波生成 74
5.1.1.1 造波方法 74
5.1.1.2 界面孤立內波的型態 75
5.1.2 實驗室內波與理論波形的比較 77
5.2 界面孤立內波在平滑底床上傳遞的物理量變化 83
5.2.1 孤立內波波形 84
5.2.1.1 影像 84
5.2.1.2 實驗結果分析與比較 94
5.2.2 孤立內波振幅 99
5.2.2.1 振幅與位能差關係圖 99
5.2.2.2 初始振幅減少率 102
5.2.2.3 振幅衰減率 105
5.2.3 孤立內波波速 108
5.2.3.1 波速變化率C(cm/s) 108
5.2.3.2 波速減少率 111
5.2.4 孤立內波波長(cm) 114
5.2.4.1 初始波長變化率 114
5.2.4.2 傳遞波長變化率 117
5.2.5 孤立內波能量 120
5.2.5.1 初始能量減少率 120
5.2.5.2 傳遞能量減少率 123
5.3 界面孤立內波在單一障礙物上傳遞的物理量變化 126
5.3.1 初始振幅減少 126
5.3.2 波速變化量C(cm/s) 127
5.3.3 波速減少率 128
5.3.4 初始能量減少 129
5.4 誤差來源探討 131
第六章 結論與建議 136
6.1 結論 136
6.2 建議 138
參考文獻 140

Apel, J.R., Holbrook, J.R., Tsai, J., and Liu, A.K., (1985). The Sulu Sea internal soliton experiment. J. Physical Oceanography, 15(12): 1625-1651.
Ariyaratnam, J., (1998). Investigation of slope stability under internal wave action. B.Eng. (Hons.) thesis, Dept. of Environmental Eng., University of Western Australia, Australia.
Baines, P.G., (1983).Tidal motion in submarine canyons – a laboratory experiment. J. Physical Oceanography, 13: 310-328.
Bogucki, D. and Garrett, C., (1993). A simple model for the shear-induced decay of an internal solitary wave. J. Physical Oceanography, 23: 1767-1776.
Bole, J.B., Ebbesmeyer, J.J., and Romea, R.D., (1994). Soliton currents in South China Sea: measurements and theoretical modelling. Proc. 26th Annual Offshore Tech. Conf., Houston, Texas, pp. 367-375.
Chen, C.C., (2004). Experimental study on the propagation and reflection of internal solitary wave from a uniform slope. Master thesis, National Sun Yat-Sen University, Taiwan.
Cheng, M.H., (2006). Numerical modeling for internal solitary wave evolution on variable topography. Master thesis, National Sun Yat-Sen University, Taiwan.
Chen, Y.C., Hsu, J.C.R., Kuo, C.F., Chen, H.H., and Cheng M.H., (2006). Laboratory observations on internal solitary wave evolution over a submarine ridge. China Ocean Engineering, 20(1): 61-72.
Chen, Y.C., Hsu, J.C.R., Chen, C.W., Chen, H.H., Kuo, C.F., and Cheng M.H., (2007a). Generation of internal solitary wave by gravity collapse. Journal of Marine Science and Technology, 15(1): 1-7.
Chen, Y.C., Hsu, J.C.R., Chen, C.W., Chen, H.H., Kuo, C.F., and Cheng M.H., (2007b). Wave propagation at the interface of a two-layer fluid system in the laboratory. Journal of Marine Science and Technology, 15(1): 8-16.
Chen, Y.C., Hsu, J.C.R., Chen, H.H., Kuo, C.F., and Cheng M.H., (2007c). Laboratory observations on internal solitary wave evolution on steep and inverse uniform slopes. Ocean Engineering, 157-170.
Chen, Y.C., Hsu, J.C.R., Cheng, M.H., Chen, H.H., and Kuo C.F., (2007d). An investigation on internal solitary waves in a two-layer fluid: Propagation and reflection from steep slopes. Ocean Engineering, 171-184.
Ekman, V.M., (1904). On dead-water. Sci. Results, Norwegian North Polar Expedition, 5(15): 1893-1896.
Farmer, D.M., (1978). Observation of long nonlinear internal waves in a lake. J. Physical Oceanography, 8(1): 63-73.
Fu, K.S., (2006). The effect of nonlinearity and mixed layer thickness on the propagation of nonlinear internal waves. thesis, National Sun Yat-Sen University, Taiwan.
Garrett, C. and Munk W., (1972). Space-time scales of internal waves. Geophysical Fluid Dyn., 3: 225-264.
Garrett, C. and Munk W., (1979). Internal waves in the ocean. Annual Review of Fluid Mechanics. 11: 339-369.
Haury, L. R., Briscoe, M.G., and Orr, M. T., (1979). Tidally generated internal wave packets in Massachusetts Bay. Nature, 278-312.
Hans, V.H., and Howarth M.J., (2004). Enhanced stability during reduction of stratification in the North Sea. Continental Shelf Research, 24: 805-819.
Helfrich, K.R. and Melville, W.K., (1986). On long nonlinear internal waves over slope-shelf topography. J. Fluid Mech., 167: 285-308.
Helfrich, K.R., (1992). Internal solitary wave breaking and run-up on a uniform slope. J. Fluid Mech., 243: 133-154.
Honji, H., Matsunaga, N., Sugihara, Y. and Sakai, K., (1995). Experimental observation of interanl symmetric solitary waves in a two-layer fluid. Fluid Dynamics Research, 15 (2): 89-102.
Hsu, M.K. and Liu, A K., (2000). Nonlinear internal waves in the South China Sea. Canadian Journal of Remote Sensing, 26: 72-81.
Hsu, M.K., Liu, A K., and Liu, C., (2000). A study of internal waves in the China Seas and Yellow Sea using SAR. Continental Shelf Research, 20: 389-410.
Hunkins, K. and Fliegel, M., (1973). Internal undular surges in Senece Lake: a natural occurrence of solitons. J. Geophysical Research, 78: 539-548.
Huttemann, H. and Hutter, K., (2001). Baroclinic solitary water waves in a two-layer fluid system with diffusive interface. Experiments in Fluids, 30(3): 317-326.
Imberger, J., (1994). Transport processes in lakes : a review. In (ed., R. Margalef) Limnology Now: A Paradigm of Planetary Problems, Amsterdam: Elsevier Science.
Johns, K., (1999). Interaction of an internal wave with a submerged sill in a two-layer fluid. B.Eng. (Hons.) thesis, Dept. of Environmental Eng., University of Western Australia, Australia.
Johnson, D.R., Weidemann, A., and Pegau, W.S., (2001). Internal tidal bores and bottom nepheloid layers. Continental Shelf Research, 21: 1473-1484.
Kao, T.W., Pan, F.S., and Renouard, D., (1985). Internal solitions on the pycnocline: generation, propagation, shoaling and breaking over a slope. J. Fluid Mech., 159: 19-53.
Koop, C.G. and Butler, G., (1981). An investigation of internal solitary waves in a two-fluid system. J. Fluid Mech., 112: 225-251.
Kuo, C.F., (2005). Experimental study on the evolution and effect of bottom obstacle on internal solitary wave. Master thesis, National Sun Yat-Sen University, Taiwan.
LeBlond, P.H. and Mysak, L.A., (1978). Waves in the Ocean. Amsterdam: Elsevier.
Liu, A.K., Holbrook, J.R., and Apel, J.R., (1985). Nonlinear internal wave evolution in the Sulu Sea. J. Physical Oceanography, 15: 1613-1624.
Lynett, P. and Liu, P.L.F., (2002). A two-dimensional depth-integrated model for internal wave propagation. Wave Motion, 36: 221-240.
Martin, A.J., Walker, S.A., and Easson, W.J., (1998). An experimental investigation of solitary internal waves. Proc. 17th Inter. Conf. Offshore Mech. & Arctic Eng., ASME.
Maxworthy, T., (1979). A note on the internal solitary waves produced by tidal flow over a three-dimensional ridge. J. Geophysical Research, 84, 338-346.
Michallet, H. and Barthelemy, E., (1997). Ultrasonic probes and data processing to study interfacial solitary waves. Experiments in Fluid, 22: 380-386.
Michallet, H. and Barthelemy, E., (1998). Experimental study of interfacial solitary waves. J. Fluid Mech., 366: 159-177.
Michallet, H. and Ivey, G.N., (1998). Experimental on mixing due to internal solitary waves breaking on uniform slopes. J. Geophysical Research, 104: 13467-13478.
Muller, P. and Liu, X., (2000).Scattering of internal waves at finite topography in two dimensions. Part Ⅱ: Spectral calculations and boundary mixing. J. Physical Oceanography, 30: 550-563.
Nagashima, H., (1971). Reflection and breaking of internal waves on a sloping beach. J. Oceanographical Society Japan, 27(1): 1-6.
Osborne, A.R., Burch, T.L., and Scarlet, T.I., (1978). The influence of internal waves on deepwater drilling . J. Petroleum Technology, 30: 1497-1504.
Osborne, A.R. and Burch, T.L., (1980). Internal solitons in the Andaman Sea. Science, 208 (4443): 451-460.
Perry, R.B. and Schimke, G.R., (1965). Large-amplitude internal waves observed off the northwest coast of Sumatra. J. Physical Oceanography, 70(10): 2319-2324.
Sapia, A. and Salusti, E., (1987). Observation of nonlinear internal solitary of the Strait of Messina. Deep Sea Research, 34(7): 1081-1092.
Small, J., Hallock, Z., Pavey, G., and Scott, J., (1999). Observations of large amplitude internal waves at the Malin Shelf edge during SESAME 1995. Continental Shelf Research, 19: 1389-1436.
Stevens, C., Lawrence, G., Hamblin, P., and Carmack, E., (1996). Wind forcing of internal waves in a long narrow stratified lake. Dynamics of Atmospheres and Oceans, 24: 41-50.
Sveen, J.K., Guo, Y., Davies, P.A., and Grue, J., (2002). On the breaking of internal solitary waves at a ridge. J. Fluid Mech., 469 (25): 161-188.
Thrope, S.A., Hall, A.J. and Croft, I., (1972). The internal surge in Loch Ness. Nature, 237: 96-98.
Thrope, S.A., (1975). The excitation, dissipation, and interaction of internal waves in the deep ocean. J. Geophysical Research, 80(3): 328-338.
Vlasenko, V. and Hutter, K., (2001). Generation of second mode solitary waves by the interaction of a first mode soliton with a sill. Nonlinear Processes in Geophysics, 8: 223-239.
Vlasenko, V. and Hutter, K., (2002). Numerical experiments on the breaking of solitary internal waves over a slope-shelf topography. J. Physical Oceanography, 32(6): 1779-1793.
Vlasenko, V., Stashchuk, N.M., and Hutter, K., (2002). Water exchange in fjords induced by tidally generated internal lee waves. Dynamics of Atmospheres and Oceans, 35: 63-89
Wessels, F. and Hutter, K., (1996). Interaction of internal waves with a topographic sill in a two-layered fluid. J.Physical Oceanography, 26 (1): 5-20.
West, B.J., (1981). Nonlinear properties of internal waves. Proceedings of American Institute of Physics, New York, 76: 353-359.