當深海一孤立內波於大陸邊緣傳遞至近岸，根據以往理論與現場文獻提及波形會由下沈型翻轉至上舉型。由兩層水體理論提出一轉折點概念，即上下層水深相等處。然受理論假設限制，鮮少探究傳遞過程中波形翻轉過程，而現場觀測受限經費不易同時獲取大範圍時空資料，故本研究將透過一連續水槽實驗與數值模式，來討論下沈型孤立內波於簡化梯形障礙物傳遞之演化。
本研究於國立中山大學內波實驗室水槽(長寬高 12*0.5 *0.7 公尺)進行相關試驗。實驗水體先放置淡水層(溫度27℃；密度996 kg/m3 )，再藉由水槽底部注入鹽水(溫度27℃；密度1030 kg/m3 )，佈置出近兩層水體。藉由重力塌陷產生出所需波形。在本研究採用四種控制因子，分別為水體特性(密躍層特徵厚度與上下層水深比)與梯形障礙物型態(前坡角與平台長度)。會採用此四種因子，由不同密躍層特徵厚度瞭解實驗室孤立內波生成與傳遞變化，改變上下層水深比討論對波形翻轉衍生影響；不同前坡角分析反射率與波形翻轉之關係；不同障礙物後平台長短對於翻轉後之波形傳遞影響。
實驗結果發現上下層水深比是引發波形翻轉最重要因子，只有由深水(上層小於下層)傳遞至平台上(上層大於下層)，超音波計所量測波形才有明顯翻轉。而密躍層特徵厚度主要影響生成孤立內波波形；當前坡角大於60°，因反射率增大導致平台上波形翻轉現象不明顯；短平台會導致似上舉型波形再次碎波，傳遞至後方能量更少。
除藉由超音波計所量得波形外，為瞭解波形翻轉時流場變化，採用數值模式模擬孤立內波於梯形障礙物傳遞。數值結果可見，波形翻轉亦造成渦動改變。換言之，原主渦動於斜坡面作用強度大幅減少，而部分能量傳入後方次要渦動中使其至平台上強度稍增。

While shoaling from deepwater in a stratified ocean, an interfacial solitary wave (ISW) may experience waveform inversion on a continental margin. Although many oceanographers have believed that the inversion from depression to elevation may commence at the turning point where the upper and bottom layers are equal in depth, this phenomenon has not been fully verified in field observations nor in a laboratory. In this study, a series of laboratory experiments and numerical modeling were conducted on the evolution of an ISW of depression across uniform slope joining a horizontal plateau which resembles pseudo slope-shelf topography, in order to clarify this fascinating phenomenon and the variations of wave properties associated with the process.
In the laboratory experiments, a depression ISW was produced by a collapse mechanism in a stratified two-layer fluid system within a steel-framed wave flume (12 m long, 0.7 m high by 0.5 m wide) at the National Sun Yat-sen University in Taiwan. The fluid density in the upper (fresh) and bottom (brine) layers was 996 and 1030 kg/m3, respectively. A series of experiments were conducted upon varying the magnitude of the most important physical factors (i.e., nominal thickness of pycnocline, depth ratio between upper and bottom layer, front gradient and shape of pseudo slope-shelf), from which the results are now discussed in four separate chapters in this thesis.
Present laboratory results indicate that the process of waveform inversion took place after an ISW had experienced internal run-down, hydraulic jump, vortex motion and surge-up on the front slope, prior to its propagation onto the plateau. Moreover, the fundamental wave period of leading wave on the plateau was significantly smaller than that in the preceding sections on the front slope and the incident stage earlier, thus representing frequency downshift. Amongst the factors involved, the depth ratio between the upper and bottom layer was the most significant one for waveform inversion. Only when the upper layer was thicker than the bottom layer on the plateau of pseudo slope-shelf, waveform inversion could occur, besides the length of the plateau. On the other hand, the front gradient and shape of pseudo slope-shelf also affected the magnitude of the transmitted wave over the plateau as the wave across this specific topography. In the case of a steeper front gradient, waveform inversion became insignificant due to stronger wave reflection and intense energy dissipation caused by turbulent mixing while a depression ISW propagated over a slope-shelf; particularly against a submerged vertical cliff. As a depression ISW across pseudo slope-shelf with short plateau, intense wave breaking might occur again with vortex motion at its rear end as the newly inversed waveform reentering deep water. In this region, the upper layer was smaller than the bottom layer, hence it could not support the continuous existence of an ISW in elevation. Again, energy dissipation occurred due to turbulent mixing beyond the rear end of a short plateau. Finally, a different mode of ISW appeared within pycnocline, while its nominal thickness was larger than the amplitude of the incident wave.
In addition to the laboratory investigations, numerical model was also adopted to study the variations in the flow field as an ISW propagated over a pseudo slope-shelf, in order to complement the experimental results. The results of numerical modeling revealed that the horizontal velocity in the bottom layer increased when the wave encountered the front slope, even if the depth of upper layer was thinner than that of the bottom layer on the plateau. Consequently, the velocity in the upper layer became less than that in the bottom layer when the former was thicker than that of the latter on the plateau. On the other hand, the vertical velocity within the self-generated vortex switched direction as waveform inversion commenced after the wave across the shoulder of pseudo slope-shelf where the local depth of the upper layer was larger than that of bottom part.
Overall, the significance of the four pertinent factors (i.e., nominal thickness of pycnocline, water depth ratio, front slope, and plateau length) that affected a depression ISW across pseudo slope-shelf is discussed in detail in this thesis, as well as the variation of flow field calculated by the numerical mode presented.

謝誌………………………………………………………………………………….i
Abstract……………………………………………………………………………ii
Chinese Abstract…………………………………………………………..…. iv
Contents…………………………………………………………………..………v
List of Figures………………………………………………………………….ix
List of Tables………………………………………………………………….xx
Nomenclature Used………………………………………………..……..xxi
Chapter 1 Introduction………………………………………………………….1
1.1 Background ………………………………………………………………….1
1.2 Literature Review……………………………………………………………..3
1.2.1 Field Observation………………………………………………………….4
1.2.2 Theoretical Analysis……………………………………………………….5
1.2.3 Laboratory Experiments………………………………………………….9
1.2.4 Numerical Modeling……………………………………………………..10
1.3 Motivation…………………………………………………………………….13
1.4 Organization of Chapters…………………………………………………..15
Chapter 2 Experimental Design……………………………………………...17
2.1 Experimental Apparatus…………………………………………………….17
2.1.1 Wave Flume…..……………………..………..……………………….…..17
2.1.2 Preparation of a Two-Layer Fluid System.………………………………..19
2.1.3 Wave Generation…………………………..……………………………...20
2.1.4 Recording Instruments……….………………………..………..………...21
2.1.4.1 Ultrasonic probes……….………………………..….…..………...21
2.1.4.2 Surface probes……….………………………..….…..……………...23
2.1.4.3 Digital video……….………………………..….…..……………...24
2.2 Physical Conditions…………….………………………..….…..………….24
2.2.1 Waveform Inversion……………..….…..………..……………………….25
2.2.1.1 Effect of nominal pycnocline thickness…….…..………..………..25
2.2.1.2 Effect of water depth ratio…………………..………………..…26
2.2.1.3 Effect of front slope……………..….…..………..………………29
2.2.1.4 Effect of plateau length……………..….……..……………….…30
2.2.3 Velocity Field of an ISW across Flat Bottom………....………..……….33
2.3 Data Processing and Analysis…….…..…………...…..…………………..…35
2.3.1 Data Processing…………..……………………..…..….…..………..........35
2.3.2 Introduction of Hilbert Transform..………..…………………………....36
Chapter 3 Effect of Nominal Pycnocline Thickness on Waveform Inversion……..………………………….................................................................41
3.1 Introduction……………………..….…..……………..…………….............42
3.2 Evolution of a Depression ISW with Broaden Pycnocline……………..…..45
3.2.1 Evolution of a Depression ISW on Flat Bottom…………………………..45
3.2.2 Evolution of a Depression ISW over Trapezoidal Obstacle………………48
3.3 Discussions on Experimental Results……………..…. ……………………49
3.3.1 Definition of Nominal Pycnocline Thickness………………….……51
3.3.2 Effect of Continuous Wave Making on Variations in Pycnocline………...53
3.3.3 Effect of Pycnocline Thickness on Variations in wave Amplitude.............60
3.3.3.1 Initial and subsequent wave amplitude on flat bottom……………...60
3.3.3.2 Transmitted wave amplitude on trapezoidal obstacle………………...63
3.3.4 Effect of Varying Pycnocline Thickness on Potential Energy………….....63
3.4 Conclusions…………..……………………………………………………..65
Chapter 4 Effect of Depth Ratio on Waveform Inversion…………….67
4.1 Introduction……………………..….…..……………..…………….............69
4.2 Numerical Model………………………………………….. ……………….73
4.3 Evolution of a Depression ISW over Trapezoidal Obstacle……………77
4.3.1 Group 1 – hs1 < hs2…………………………………….…………………77
4.3.2 Group 2 – hs1 = hs2………………………………………….…………80
4.3.3 Group 3 – hs1 > hs2……………………………………..…….…………83
4.3.3.1 Incident wave with moderate amplitude…….…………………….83
4.3.3.2 Incident wave with large amplitude…………………………….…..85
4.4 Comparison on Results……………………………………………………..89
4.4.1 Dimensionless Parameters………………………………………………89
4.4.2 Waveform Instability……………………………………………………92
4.4.3 Amplitude Ratio of Crest to Trough…………………………….…….…94
4.4.4 Characteristic Wavelength Ratios………………….…………………….100
4.4.5 Variation in Mean Wave Speed………………………………………….103
4.4.6 Transmitted Potential Wave Energy…………………………………..…104
4.5 Conclusions……………………………………………………………..…106
Chapter 5 Effect of Front Slope on Waveform inversion…………….113
5.1 Introduction……………………..….…..……………..…………….............114
5.2 ISW of Depression across Trapezoidal Obstacle………………………119
5.2.1 Waveform Evolution on Mild Slope of 13 Degrees……………………..119
5.2.2 Waveform Evolution on Steep Slope of 45 and 60 Degrees…………….122
5.2.3 Waveform Evolution against a Vertical Front Slope…………………….123
5.2.4 Comparison on Experimental Results with Different Front Slopes……..125
5.3 Discussion on Experimental Results………………………………………132
5.3.1 Variation in Wave Amplitude with Front Slope…………………….…...134
5.3.2 Variation in Crest and Trough Height………………………………..….135
5.3.3 Variation in Characteristic Period..………………………………....137
5.3.4 Variation in Transmitted Wave Energy………………………..…………145
5.4 Analysis of Digital Video Imagery………………………………………..151
5.5 Conclusions…………………………………………………………….….153
Chapter 6 Effect of Plateau Length on Waveform Inversion….…….157
6.1 Introduction……………………..….…..……………..…………….............158
6.2 Evolution of a Depression ISW over Trapezoidal Obstacle…………….161
6.2.1 Process of Wave from Evolution on the Front Slope………………….161
6.2.2 Waveform Evolution across Long or Short Plateau……………………164
6.2.3 Wave Evolution beyond the Rear end of Short Plateau………………...169
6.3 Results and Discussions……………………………………………………173
6.3.1 Waveform Inversion…………………………………………………..…175
6.3.2 Variation in Crest and Trough Height……………………………….…..178
6.3.3 Variation in Characteristic Wavelength……………………….…………180
6.3.4 Variation in Transmitted Phase Speed…………………………………..183
6.3.5 Variation in Transmitted Wave Energy…………………………………184
6.4 Comparison on Flow Field among Different Obstacle Shapes………….188
6.5 Conclusions………………………………………………………………….195
Chapter 7 Flow Field of an ISW Evolution on Flat Bottom…………199
7.1 Introduction……………………..….…..……………..…………….............199
7.2 Results of Laboratory Experiments…………………………………….….201
7.2.1 Orbital Paths for a Depression ISW on Flat Bottom……………………201
7.2.2 Orbital Paths for an Elevation ISW on Flat Bottom……………………208
7.2.3 Velocity Field of Different Bead Sizes……..……………………………213
7.3 Results of Theoretical Flow Field…………..................................................215
7.3.1 Governing Equations……………............................................................215
7.3.2 Theoretical Results of Flow Field…........................................................220
7.3.3 Theoretical Results using other Expression........................................223
7.4 Conclusions……….........................................................................................228
Chapter 8 Flow Field of an ISW Evolution over Slope-Shelf…..……231
8.1 Introduction……………………..….…..……………..…………….............231
8.2 Theoretical Calculation with Laboratory Results………………………..233
8.2.1 Practical Consideration…………….………………………..……..….233
8.2.2 Results of Theoretical Calculations.……………………………………..235
8.2.2.1 Group 1: hs1 < hs2 …………....……………………………………235
8.2.2.2 Group 3: hs1 > hs2 …………....…………………………………....240
8.3 4 Numerical Modeling………………………………………………...........244
8.3.1 Governing Equations…………………………………………….............244
8.3.2 Results of Numerical Modeling………………………………………....245
8.3.2.1 Group 1: hs1 < hs2 …………....……………………………………246
8.3.2.2 Group 3: hs1 > hs2 …………....…………………………………....252
8.4 Conclusions……….........................................................................................257
Chapter 9 Conclusions………..………………………….....….…………….263
References………..………………………….....….……………………………..269
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