The course readings are described below. The key to the abbreviations in the Readings column is provided below.

## Readings Legend

[W] White, F. *Viscous Fluid Flo*w. McGraw-Hill, 1991. ISBN:0-07-069712-4.

[B] Batchelor, G. K. *An Introduction to Fluid Dynamics*. Cambridge University Press, 2000. ISBN:0-521-66396-2.

[C&B] Cebeci, T., and P. Bradshaw. *Momentum Transfer in Boundary Layers*. McGraw-Hill, 1977. ISBN:0-07-010300-3.

[S] Schlichting, H et al. *Boundary Layer Theory, 8th Ed*. Springer Verlag, 1999. ISBN: 3540662707.

[R] Rosenhead, L. *Laminar Boundary Layers*. Dover Publications, 1988. ISBN:0-486-65646-2.

[B,C&W] Bradshaw, Cebeci, and Whitelaw. *Engineering Calculation Methods for Turbulent Flow*. Academic Press, 1981. ASIN:0121245500.

[K&C] Kuethe, A. and C-Y. Chow. *Foundations of Aerodynamics, 4th Ed*. John Wiley & Sons, 1986. ASIN:0471509531.

LEC # | TOPICS | READINGS |
---|---|---|

Underlying Physical Principles |
||

1 | Course Description. Fundamental Theorem of Kinematics - Convection, Vorticity, Strain. | [B] 78-87 [W] 16-22 |

2 | Eulerian vs. Langrangian Description. Convection Relations. | |

Conservation Laws |
||

3 | Conservation of Mass. Conservation of Momentum. Stress Tensor. | [B] 73-75, 137-151 [S] 47-61 [W] 61-65 |

4 | Viscosity. Newtonian Fluids. Vorticity and Circulation. | [W] 23-29, 59-69, 89-91 [K&C] 40-50 [B] 71-99 |

5 | Navier-Stokes Equations. Physical Parameters. Dynamic Similarity. |
[B] 164-173 |

Thin Shear Layer Approximation |
||

6 | Dimensional Analysis. Dominant Balance and Vscous Flow Classification. | [W] 81-88, 94, 104-107, 114-119, 132-141 [S] 13-18 |

7 | Re→∞ Behavior. Thin Shear Layer Equations. TSL Coordinates. |
[S] 96-99, 145-148 [W] 218-219, 227-233 |

8 | TSL Coordinates. Boundary Conditions. Shear Layer Categories. | |

9 | Local Scaling. Falkner-Skan Flows. | [B] 308-314 [S] 201-206 [W] 233-246 |

Solution Techniques |
||

10 | ODE'S, PDE's, and Boundary Conditions. Well-Posedness. | [W] 77-78 Tannehill, Anderson and Pletcher. Computational Fluid Mechanics And Heat Transfer, 2nd Ed. Taylor and Francis, 1997. Pp. 19-31. |

11 | Numerical Methods for ODE's. Discretization. Stability. | Hirsch, C. Numerical Computation of Internal and External Flows. Vol. 1. John Wiley & Sons, 1989. Pp. 267-290.Tannehill, Anderson and Pletcher. Pp. 76-83. |

12 | Finite Difference Methods. Newton-Raphson. | |

13 | Integral Methods. Integral Momentum Equation. Thwaites' Method. | [W] 264-274 [S] 191-202 (682-698 Optional) [C&B] 104-116 |

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. | |

18 | IBLT Solution Techniques. Iteration Stability. | |

19 | Fully-Coupled Iteration. 3-D IBLT. | [S] 449-483 [W] 335-355 |

Stability and Transition |
||

20 | Small-Perturbation Theory. Orr-Sommerfeld Equation. | [S] 449-483 [W] 335-355 |

21 | Small-Perturbation Theory. Orr-Sommerfeld Equation. (cont.) | |

22 | Boundary Conditions, Homogeneity, Solution Techniques. | [S] 434-473 [C&B] 290-301 |

23 | Transition Mechanisms. Transition Prediction: Local Correlations, Amplification Methods. | [S] [W] |

Turbulent Shear Layers |
||

24 | Reynolds Averaging. Prandtl's Analogy. | [S] 496-538 [W] 394-463 [C&B] |

25 | Turbulent BL Structure: Wake, Wall Layers. Inner, Outer Variables. Effects of Roughness. | [S] 495-552 [C&B] 160-210 [W] 394-449 |

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.) | |

29 | Turbulence Modeling and Closure. Algebraic Models. Transport Models. | |

Compressible Thin Shear Layers |
||

30 | Definition and Implications of Compressibility. Special Solutions. Reynolds Analogy. | [S] 327-330, 340-352 [W] 184-200, 576-616 |

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. | |

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. | [W] 342-344 Reed, H.L. and W.S. Saric, "Stability of Three-Dimensional Boundary Layers". Annual Review of Fluid Mechanics 21 (1989): 235 - 284. Mack, L.M. "Boundary-layer stability theory", Special Course on Stability and Transition of Laminar Flow, AGARD R-709 (1984): 3-1 - 3-81. |