| Underlying Physical Principles |
| 1 | Course Description. Fundamental Theorem of Kinematics - Convection, Vorticity, Strain. | |
| 2 | Eulerian vs. Langrangian Description. Convection Relations. | Assignment #1 Out |
| Conservation Laws |
| 3 | Conservation of Mass. Conservation of Momentum. Stress Tensor. | |
| 4 | Viscosity. Newtonian Fluids. Vorticity and Circulation | |
| 5 | Navier-Stokes Equations. Physical Parameters. Dynamic Similarity. | Assignment #1 Due |
| Thin Shear Layer Approximation |
| 6 | Dimensional Analysis. Dominant Balance and Viscous Flow Classification. | Assignment #2 Out |
| 7 | Re→∞ Behavior. Thin Shear Layer Equations. TSL Coordinates. | |
| 8 | TSL Coordinates. Boundary Conditions. Shear Layer Categories. | |
| 9 | Local Scaling. Falkner-Skan Flows. | Assignment #2 Due
Assignment #3 Out |
| Solution Techniques |
| 10 | ODE'S, PDE's, and Boundary Conditions. Well-posedness. | |
| 11 | Numerical Methods for ODE's. Discretization. Stability. | Assignment #3 Due |
| 12 | Finite Difference Methods. Newton-Raphson. | |
| 13 | Integral Methods. Integral Momentum Equation. Thwaites' Method. | Assignment #4 Out |
| 14 | Integral Kinetic Energy Equation. Dissipation Methods. | |
| 15 | Integral Kinetic Energy Equation. Dissipation Methods. (cont.) | |
| Interacting Boundary Layer Theory |
| 16 | Asymptotic Perturbation Theory. Higher-Order Effects. | |
| 17 | 2D Interaction Models: Displacement Body, Transpiration. Form Drag, Stall Mechanisms. | Assignment #4 Due |
| 18 | IBLT Solution Techniques. Iteration Stability. | Assignment #5 Out |
| 19 | Fully-coupled Iteration. 3-D IBLT. | |
| Stability and Transition |
| 20 | Small-perturbation Theory. Orr-Sommerfeld Equation. | |
| 21 | Small-perturbation Theory. Orr-Sommerfeld Equation. (cont.) | |
| 22 | Boundary Conditions, Homogeneity, Solution Techniques. | |
| 23 | Transition Mechanisms. Transition Prediction: Local Correlations, Amplification Methods. | Assignment #5 Due |
| Turbulent Shear Layers |
| 24 | Reynolds Averaging. Prandtl's Analogy. | Assignment #6 Out |
| 25 | Turbulent BL Structure: Wake, Wall layers. Inner, Outer Variables. Effects of Roughness. | |
| 26 | Turbulent BL Structure: Wake, Wall layers. Inner, Outer Variables. Effects of Roughness. (cont.) | |
| 27 | Equilibrium BL's: Clauser Hypothesis. Dissipation Formulas and Integral Closure. | |
| 28 | Equilibrium BL's: Clauser Hypothesis. Dissipation Formulas and Integral Closure. (cont.) | Assignment #6 Due |
| 29 | Turbulence Modeling and Closure. Algebraic Models. Transport Models. | |
| Compressible Thin Shear Layers |
| 30 | Definition and Implications of Compressibility. Special Solutions. Reynolds Analogy. | |
| 31a | Definition and Implications of Compressibility. Special Solutions. Reynolds Analogy. (cont.) | |
| 31b | Approximate Temperature Profile. Reynolds Heat Flux. | |
| 3D Boundary Layer |
| 32 | New effects: Crossflow, Lateral Dilation, 3D Separation. Governing Equations. | |
| 33 | Coordinate Systems. Characteristics, BC's, and Well-posedness. | Assignment #8 Out |
| 34 | 3D Characteristics, BC's. Quasi-3D: Constant-crossflow Approximation. | |
| 35 | 3D Characteristics, BC's. Quasi-3D: Constant-crossflow Approximation.(cont.) | |
| 36 | 3D Stability Theory. 3D Transition Mechanisms. | Assignment #8 Due |