Stability of Fluid Motions I
The study of stability aims at understanding the abrupt changes which are observed in fluid motions as the external parameters are varied. It is a demanding study, far from full grown"whose most interesting conclusions are recent. I have written a detailed account of those parts of the recent t...
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
1976, 1976
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| Edition: | 1st ed. 1976 |
| Series: | Springer Tracts in Natural Philosophy
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- § 29. Steady Causes and Steady Effects
- § 30. Laminar and Turbulent Comparison Theorems
- § 31. A Variational Problem for the Least Pressure Gradient in Statistically Stationary Turbulent Poiseuille Flow with a Given Mass Flux Discrepancy
- § 32. Turbulent Plane Poiseuille Flow—a Lower Bound for the Response Curve
- § 33. The Response Function Near the Point of Bifurcation
- § 34. Construction of the Bifurcating Solution
- § 35. Comparison of Theory and Experiment
- Notes for Chapter IV
- V. Global Stability of Couette Flow between Rotating Cylinders
- § 36. Couette Flow, Taylor Vortices, Wavy Vortices and Other Motions which Exist between the Cylinders
- § 37. Global Stability of Nearly Rigid Couette Flows
- § 38. Topography of the Response Function, Rayleigh’s Discriminant..
- § 39. Remarks about Bifurcation and Stability
- § 40. Energy Analysis of Couette Flow; Nonlinear Extension of Synge’s Theorem
- VII. Global Stability of the Flow between Concentric Rotating Spheres
- § 53. Flow and Stability of Flow between Spheres
- Appendix A. Elementary Properties of Almost Periodic Functions
- Appendix B. Variational Problems for the Decay Constants and the Stability Limit
- B 1. Decay Constants and Minimum Problems
- B 2. Fundamental Lemmas of the Calculus of Variations
- B 6. Representation Theorem for Solenoidal Fields
- B 8. The Energy Eigenvalue Problem
- B 9. The Eigenvalue Problem and the Maximum Problem
- Notes for Appendix B
- Appendix C. Some Inequalities
- Appendix D. Oscillation Kernels
- Appendix E. Some Aspects of the Theory of Stability of Nearly Parallel Flow
- E 1. Orr-Sommerfeld Theory in a Cylindrical Annulus
- E 2. Stability and Bifurcation of Nearly Parallel Flows
- References
- III. Poiseuille Flow: The Form of the Disturbance whose Energy Increases Initially at the Largest Value of v
- § 17. Laminar Poiseuille Flow
- § 18. The Disturbance Flow
- § 19. Evolution of the Disturbance Energy
- § 20. The Form of the Most Energetic Initial Field in the Annulus
- § 21. The Energy Eigenvalue Problem for Hagen-Poiseuille Flow
- § 22. The Energy Eigenvalue Problem for Poiseuille Flow between Concentric Cylinders
- § 23. Energy Eigenfunctions—an Application of the Theory of Oscillation kernels
- § 24. On the Absolute and Global Stability of Poiseuille Flow to Disturbances which are Independent of the Axial Coordinate
- § 25. On the Growth, at Early Times, of the Energy of the Axial Component of Velocity
- § 26. How Fast Does a Stable Disturbance Decay
- IV. Friction Factor Response Curves for Flow through Annular Ducts
- § 27. Responce Functions andResponse Functionals
- § 28. The Fluctuation Motion and the Mean Motion
- 1. Global Stability and Uniqueness
- § 1. The Initial Value Problem and Stability
- §2. Stability Criteria—the Basic Flow
- § 3. The Evolution Equation for the Energy of a Disturbance
- § 4. Energy Stability Theorems
- § 5. Uniqueness
- Notes for Chapter I
- II. Instability and Bifurcation
- § 6. The Global Stability Limit
- § 7. The Spectral Problem of Linear Theory
- § 8. The Spectral Problem and Nonlinear Stability
- § 9. Bifurcating Solutions
- § 10. Series Solutions of the Bifurcation Problem
- § 11. The Adjoint Problem of the Spectral Theory
- § 12. Solvability Conditions
- § 13. Subcritical and Supercritical Bifurcation
- § 14. Stability of the Bifurcating Periodic Solution
- § 15. Bifurcating Steady Solutions; Instability and Recovery of Stability of Subcritical Solutions
- § 16. Transition to Turbulence by Repeated Supercritical Bifurcation
- Notes for Chapter II
- § 41. The Optimum Energy Stability Boundary for Axisymmetric Disturbances of Couette Flow
- § 42. Comparison of Linear and Energy Limits
- VI. Global Stability of Spiral Couette-Poiseuille Flows
- § 43. The Basic Spiral Flow. Spiral Flow Angles
- § 44. Eigenvalue Problems of Energy and Linear Theory
- § 45. Conditions for the Nonexistence of Subcritical Instability
- § 46. Global Stability of Poiseuille Flow between Cylinders which Rotate with the Same Angular Velocity
- § 47. Disturbance Equations for Rotating Plane Couette Flow
- § 48. The Form of the Disturbance Whose Energy Increases at the Smallest R
- § 49. Necessary and Sufficient Conditions for the Global Stability of Rotating Plane Couette Flow
- § 50. Rayleigh’s Criterion for the Instability of RotatingPlane Couette Flow, Wave Speeds
- § 51. The Energy Problem for Rotating Plane Couette Flow when Spiral Disturbances are Assumed from the Start
- § 52. Numerical and Experimental Results