Stability of Parallel Flows

1st Edition - January 1, 1967
Author: R. Betchov
Language: English
eBook ISBN:
9 7 8 - 0 - 3 2 3 - 1 6 2 6 0 - 9

Stability of Parallel Flows provides information pertinent to hydrodynamical stability. This book explores the stability problems that occur in various fields, including… Read more

Purchase options

LIMITED OFFER

Save 50% on book bundles

Immediately download your ebook while waiting for your print delivery. No promo code is needed.

Institutional subscription on ScienceDirect

Request a sales quote

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.

PrefaceAcknowledgmentKey to NotationIntroductionPart 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 WakesPart 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 FlowsAppendix I. Errors in Numerical ProcedureAppendix II. On Analytic Solutions of the Orr-Sommerfeld EquationAppendix III. Technique of OrthogonalizationReferences CitedAdditional BibliographyAuthor IndexSubject Index