Unsteady Viscous Flows

1. Basic Concepts.- 1.1 Introduction.- 1.2 The Governing Equations.- 1.3 Characteristics.- 1.4 Subcharacteristics.- 1.5 Navier-Stokes versus Euler and Prandtl.- 1.6 Zones of Influence and Dependence.- 1.7 Existence, Uniqueness, and Bounds.- 2. Numerical Analysis.- 2.1 Introduction.- 2.2 Convergence.- 2.3 Stability.- 2.4 Consistency and the Equivalence Theorem.- 2.5 Unsteady Flow Equations.- 2.6 Implicit Schemes.- 2.7 The Keller-Box Method.- 2.8 Upwind Differencing.- 2.9 Navier-Stokes-Lattices and Boundary Conditions.- 3. Impulsive Motion.- 3.1 Introduction.- 3.2 The Flow Immediately after an Impulsive Start.- 3.3 An Order of Magnitude Analysis.- 3.4 Infinite Bodies-Rayleigh Problems.- 3.5 Pointed Bodies Started Impulsively.- 3.6 Blunt Bodies Started Impulsively.- 3.7 Solutions to the Full Navier-Stokes Equations.- 3.8 Results and Physical Interpretation.- 3.9 A Computer Program.- 4. Oscillations with Zero Mean.- 4.1 Introduction.- 4.2 Oscillations of an Infinite Flat Plate.- 4.3 Oscillations of a Blunt Body.- 4.4 The Streaming Layer.- 4.5 Inner and Outer Expansions.- 4.6 Typical Results.- 5. Oscillating Flows with Non-Vanishing Mean.- 5.1 Introduction.- 5.2 Perturbation Methods.- 5.3 The Method of Averaging.- 5.4 The Boundary Layer Approximation.- 5.5 Numerical Results and Their Physical Significance.- 5.6 Nonlinear Effects.- 5.7 Traveling Waves.- 6. Unsteady Turbulent Flows.- 6.1 Introduction.- 6.2 The Triple Decomposition.- 6.3 Algebraic Models.- 6.4 One- and Two-Equation Models.- 6.5 Numerical Results and Experimental Data.- 6.6 A Computer Program.- 7. Unsteady Separation.- 7.1 Introduction.- 7.2 Separation over Moving Walls.- 7.3 Asymptotic Methods.- 7.4 Semisimilar Solutions.- 7.5 Direct Numerical Integration-Impulsive and Transient Changes.- 7.6 LagrangianFormulation.- 7.7 The Emergence of Separation.- 7.8 Wakes.- 7.9 A Computer Program.