Most of the fundamental concepts of unsteady viscous flows have been known since the early part of the century. However, the past decade has seen an unprecedented number of publications in this area. In this monograph I try to connect materials of earlier contributions and synthesize them into a comprehensive entity. One of the main purposes of a monograph, in my opinion, is to fit together in a comprehensive way scattered contributions that provide fragmented information to the readers. The collection of such contributions should be presented in a unified way; continuity of thought and logical sequence of the presentation of ideas and methods are essential. The reader should be able to follow through without having to resort to other references, something that is unavoidable in the case of a research paper or even a review paper. Many of the solutions discussed in the literature address specific practical problems. In fact, in the process of collecting information, I discovered independent lines of investigations, dealing with the same physical problem, but inspired by different practical applications. For example, I found that two groups of investigators have been studying independently the response of a viscous layer to a harmonic external disturbance. One group is con­ cerned with mass transport and the transport of sediment over the bottom of the ocean, and the other is interested in the aerodynamics of lifting surfaces in harmonically changing environments.

Inhalt

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.- References.- 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.- References.- 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.- References.- 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.- References.- 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.- References.- 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.- References.- 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 Lagrangian Formulation.- 7.7 The Emergence of Separation.- 7.8 Wakes.- 7.9 A Computer Program.- References.