Stability of Parallel Flows - 1st Edition - ISBN: 9780123957719, 9780323162609

Stability of Parallel Flows

1st Edition

Authors: R. Betchov
eBook ISBN: 9780323162609
Imprint: Academic Press
Published Date: 1st January 1967
Page Count: 344
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Stability of Parallel Flows provides information pertinent to hydrodynamical stability. This book explores the stability problems that occur in various fields, including electronics, mechanics, oceanography, administration, economics, as well as naval and aeronautical engineering. Organized into two parts encompassing 10 chapters, this book starts with an overview of the general equations of a two-dimensional incompressible flow. This text then explores the stability of a laminar boundary layer and presents the equation of the inviscid approximation. Other chapters present the general equations governing an incompressible three-dimensional flow, which requires the massive use of a computer. This book discusses as well the experimental studies on the oscillations of the boundary layer wherein the mean flow is affected by the presence of oscillations. The final chapter describes the concept of the stability of turbulent flows found in boundary layers, wakes, and jets. This book is a valuable resource for physicists, mathematicians, engineers, scientists, and researchers.

Table of Contents



Key to Notation


Part One: Initiation to Two-Dimensional Problems

Chapter I General Equations and Inviscid Cases

1. General Equations

2. Pressure, Vorticity, Energy

3. Oscillations of a Uniform Stream

4. Oscillations of Two Adjacent Uniform Streams

5. The Inviscid Shear Layer

6. Inviscid Jets and Wakes

Chapter II Simplified Analysis of the Boundary Layer

7. Generalities and Boundary Conditions

8. The Inviscid Solution

9. Friction at the Wall

10. The Critical Layer

11. Final Results for Boundary Layers

12. The Unstable Boundary Layer

Chapter III Machine Analysis of Viscous Flows

13. The Viscous Shear Layer

14. The Boundary Layer

15. Channel Flows

16. Viscous Jets and Wakes

Part Two: The General Problem

Chapter IV General Analysis of Oscillating Flows

17. Three-Dimensional Governing Equations

18. Equivalent Transformations

19. The Squire Theorem

20. Some Properties of Inviscid Oscillations

21. Some Properties of Viscous Oscillations

22. Stability Surfaces

Chapter V The Initial Value Problem

23. Formulation of the Problem

24. An Example of the Initial Problem

Chapter VI Experiments

25. Experiments Confirming Theory

26. Experiments Related to Subsequent Development of Instability

Chapter VII Nonlinear Effects

27. Theory of Longitudinal Vortices

28. Theory of Nonlinear Critical Layer

29. Analytic Studies of Nonlinear Processes

30. Numerical Experiments with Distributed Vortices

31. Numerical Experiments with Discrete Vortices

32. The Energy Method

Chapter VIII Compressibility and Fluid Stratification Effects

33. Generalities

34. Thermodynamic Preliminaries

35. The Mean Flow of a Perfect Gas

36. Inviscid Fluctuations

37. The Free Stream

38. Inviscid Shear Flow

39. Effects of Viscosity and Heat Conduction

40. Free-Stream Modes with Viscosity and Heat Conduction

41. The Two-Dimensional Supersonic Boundary Layer

42. Subsonic Oscillations in Stratified Layers

43. Three-Dimensional Compressible Effects

Chapter IX Magnetohydrodynamic Effects

44. General Equations

45. The Two-Dimensional Problem

46. Magnetohydrodynamic Squire Theorem

47. The Free Stream

48. Shear Flows and Magnetic Gradients

49. The Low Magnetic Reynolds Number Approximation

50. The Magnetic Critical Layer

51. The Oblique Magnetic Field

52. Magnetohydrodynamic Energy Equation

Chapter X Additional Topics and Complexities

53. Spatially Growing Oscillations

54. Quasi-Parallel Mean Flows

55. Forecasting Transition

56. Axisymmetric Flows

57. Flexible Boundaries

58. The Effect of Centrifugal Forces

59. Variable Mean Viscosity and Fluctuations

60. Viscoelastic Flows and Dusty Gases

61. Turbulent Flows

Appendix I. Errors in Numerical Procedure

Appendix II. On Analytic Solutions of the Orr-Sommerfeld Equation

Appendix III. Technique of Orthogonalization

References Cited

Additional Bibliography

Author Index

Subject Index


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© Academic Press 1967
Academic Press
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About the Author

R. Betchov

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