Stability of Fluid Motions I

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.- 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.-
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.-
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.- 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.