基本物理學原理
Underlying Physical Principles
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| 1 |
課程敘述，動力學基本理論-對流，渦旋量，應變。
Course Description. Fundamental Theorem of Kinematics - Convection, Vorticity, Strain. |
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| 2 |
流場質點運動描述法：歐拉 vs. 拉格朗基描述法。
對流關係。
Eulerian vs. Langrangian Description. Convection Relations.
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出作業1
Assignment #1 Out
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守恆定律
Conservation Laws
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| 3 |
質量守恆，動量守恆，應力張量。
Conservation of Mass. Conservation of Momentum. Stress Tensor.
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| 4 |
黏滯性，牛頓流體，渦旋量，和環流量。
Viscosity. Newtonian Fluids. Vorticity and Circulation
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| 5 |
納維埃-司托克斯(N-S)方程式，物理參數，動力相似。
Navier-Stokes Equations. Physical Parameters. Dynamic Similarity.
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交作業1
Assignment #1 Due
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薄剪力層近似求解
Thin Shear Layer Approximation
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| 6 |
因次分析。優勢平衡和黏滯流分類。
Dimensional Analysis. Dominant Balance and Viscous Flow Classification.
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出作業2
Assignment #2 Out
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| 7 |
Re雷諾數很大的極限情況，剪力薄層方程式，薄剪力層座標。
→∞ Behavior. Thin Shear Layer Equations. TSL Coordinates.
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| 8 |
薄剪力層座標，邊界條件，剪力層種類。
TSL Coordinates. Boundary Conditions. Shear Layer Categories. |
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| 9 |
局部尺寸，福克納-史坎流。
Local Scaling. Falkner-Skan Flows.
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交作業2
Assignment #2 Due
出作業3
Assignment #3 Out
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求解技巧
Solution Techniques
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常微分方程，偏微分方程和邊界條件，最佳適切性
ODE'S, PDE's, and Boundary Conditions. Well-posedness.
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| 11 |
常微分方程的數值方法，離散穩定性。
Numerical Methods for ODE's. Discretization. Stability.
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交作業3
Assignment #3 Due
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| 12 |
有限差分法，牛頓-拉夫生法
Finite Difference Methods. Newton-Raphson.
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| 13 |
積分方法。積分動量方程式。Thwaites' 積分法。
Integral Methods. Integral Momentum Equation. Thwaites' Method.
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出作業4
Assignment #4 Out
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積分動能方程式。消散方法。
Integral Kinetic Energy Equation. Dissipation Methods.
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積分動能方程式。消散方法。(接續)
Integral Kinetic Energy Equation. Dissipation Methods. (cont.)
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邊界層的互動理論
Interacting Boundary Layer Theory
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漸近擾動理論-高階效應。
Asymptotic Perturbation Theory. Higher-Order Effects.
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| 17 |
二維互動模式：位移物體，蒸散，形狀阻力，失速機制。
2D Interaction Models: Displacement Body, Transpiration. Form Drag, Stall Mechanisms.
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交作業4
Assignment #4 Due
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邊界層的互動理論的求解技巧。疊代穩定性。
IBLT Solution Techniques. Iteration Stability.
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出作業5
Assignment #5 Out
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| 19 |
全偶合疊代。三維的互動的邊界層理論。
Fully-coupled Iteration. 3-D IBLT.
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穩定和過渡
Stability and Transition
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小擾動理論。奧-索末非方程。
Small-perturbation Theory. Orr-Sommerfeld Equation.
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小擾動理論。奧-索末非方程。(接續)
Small-perturbation Theory. Orr-Sommerfeld Equation. (cont.)
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邊界條件，齊次性，求解技巧。
Boundary Conditions, Homogeneity, Solution Techniques.
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過渡機制。過渡預測。局部相關性，放大法。
Transition Mechanisms. Transition Prediction: Local Correlations, Amplification Methods.
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交作業5
Assignment #5 Due
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紊流剪力層
Turbulent Shear Layers
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雷諾平均。蒲朗多相似。
Reynolds Averaging. Prandtl's Analogy.
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出作業6
Assignment #6 Out
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紊流邊界層結構：尾流，壁面層，內、外變數。粗糙度效應。
Turbulent BL Structure: Wake, Wall layers. Inner, Outer Variables. Effects of Roughness.
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| 26 |
紊流邊界層結構：尾流，壁面層，內、外變數。粗糙度效應。(接續)
Turbulent BL Structure: Wake, Wall layers. Inner, Outer Variables. Effects of Roughness. (cont.)
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平衡邊界層：克勞勒假說。消散公式和封閉積分。
Equilibrium BL's: Clauser Hypothesis. Dissipation Formulas and Integral Closure.
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| 28 |
平衡邊界層：克勞勒假說。消散公式和封閉積分。(接續)
Equilibrium BL's: Clauser Hypothesis. Dissipation Formulas and Integral Closure. (cont.)
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交作業6
Assignment #6 Due
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| 29 |
紊流模式與封閉性。代數模式。傳輸模式。
Turbulence Modeling and Closure. Algebraic Models. Transport Models.
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可壓縮薄剪力層
Compressible Thin Shear Layers
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| 30 |
可壓縮性的定義與含意，特解。雷諾相似。
Definition and Implications of Compressibility. Special Solutions. Reynolds Analogy.
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| 31a |
可壓縮性的定義與含意，特解。雷諾相似。(接續)
Definition and Implications of Compressibility. Special Solutions. Reynolds Analogy. (cont.)
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| 31b |
近似溫度分布。雷諾熱通量。
Approximate Temperature Profile. Reynolds Heat Flux.
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三維邊界層
3D Boundary Layer
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| 32 |
新的效應：交叉流動，側向擴張，三維分離，統御方程式。
New effects: Crossflow, Lateral Dilation, 3D Separation. Governing Equations.
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| 33 |
座標系統。特徵，邊界條件，和最佳適切性。
Coordinate Systems. Characteristics, BC's, and Well-posedness.
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出作業8
Assignment #8 Out
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| 34 |
三維特徵，邊界條件，準三維：交流常數近似解。
3D Characteristics, BC's. Quasi-3D: Constant-crossflow Approximation.
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| 35 |
三維特徵，邊界條件，準3-D：交流常數近似解。(接續)
3D Characteristics, BC's. Quasi-3D: Constant-crossflow Approximation.(cont.)
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| 36 |
三維穩定性理論。三維過渡機制。
3D Stability Theory. 3D Transition Mechanisms.
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交作業8
Assignment #8 Due
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