Stability of Parallel Flows

Stability of Parallel Flows

1st Edition - January 1, 1967

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  • Author: R. Betchov
  • eBook ISBN: 9780323162609

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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

  • Preface


    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

Product details

  • No. of pages: 344
  • Language: English
  • Copyright: © Academic Press 1967
  • Published: January 1, 1967
  • Imprint: Academic Press
  • eBook ISBN: 9780323162609

About the Author

R. Betchov

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