Author | Joseph, Daniel D. author |
---|---|
Title | Stability of Fluid Motions I [electronic resource] / by Daniel D. Joseph |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1976 |
Connect to | http://dx.doi.org/10.1007/978-3-642-80991-0 |
Descript | XIV, 282 p. online resource |
1. Global Stability and Uniqueness -- ยง 1. The Initial Value Problem and Stability -- ยง2. Stability Criteriaโthe Basic Flow -- ยง 3. The Evolution Equation for the Energy of a Disturbance -- ยง 4. Energy Stability Theorems -- ยง 5. Uniqueness -- Notes for Chapter I -- II. Instability and Bifurcation -- ยง 6. The Global Stability Limit -- ยง 7. The Spectral Problem of Linear Theory -- ยง 8. The Spectral Problem and Nonlinear Stability -- ยง 9. Bifurcating Solutions -- ยง 10. Series Solutions of the Bifurcation Problem -- ยง 11. The Adjoint Problem of the Spectral Theory -- ยง 12. Solvability Conditions -- ยง 13. Subcritical and Supercritical Bifurcation -- ยง 14. Stability of the Bifurcating Periodic Solution -- ยง 15. Bifurcating Steady Solutions; Instability and Recovery of Stability of Subcritical Solutions -- ยง 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 -- ยง 17. Laminar Poiseuille Flow -- ยง 18. The Disturbance Flow -- ยง 19. Evolution of the Disturbance Energy -- ยง 20. The Form of the Most Energetic Initial Field in the Annulus -- ยง 21. The Energy Eigenvalue Problem for Hagen-Poiseuille Flow -- ยง 22. The Energy Eigenvalue Problem for Poiseuille Flow between Concentric Cylinders -- ยง 23. Energy Eigenfunctionsโan Application of the Theory of Oscillation kernels -- ยง 24. On the Absolute and Global Stability of Poiseuille Flow to Disturbances which are Independent of the Axial Coordinate -- ยง 25. On the Growth, at Early Times, of the Energy of the Axial Component of Velocity -- ยง 26. How Fast Does a Stable Disturbance Decay -- IV. Friction Factor Response Curves for Flow through Annular Ducts -- ยง 27. Responce Functions and Response Functionals -- ยง 28. The Fluctuation Motion and the Mean Motion -- ยง 29. Steady Causes and Steady Effects -- ยง 30. Laminar and Turbulent Comparison Theorems -- ยง 31. A Variational Problem for the Least Pressure Gradient in Statistically Stationary Turbulent Poiseuille Flow with a Given Mass Flux Discrepancy -- ยง 32. Turbulent Plane Poiseuille Flowโa Lower Bound for the Response Curve -- ยง 33. The Response Function Near the Point of Bifurcation -- ยง 34. Construction of the Bifurcating Solution -- ยง 35. Comparison of Theory and Experiment -- Notes for Chapter IV -- V. Global Stability of Couette Flow between Rotating Cylinders -- ยง 36. Couette Flow, Taylor Vortices, Wavy Vortices and Other Motions which Exist between the Cylinders -- ยง 37. Global Stability of Nearly Rigid Couette Flows -- ยง 38. Topography of the Response Function, Rayleighโs Discriminant.. -- ยง 39. Remarks about Bifurcation and Stability -- ยง 40. Energy Analysis of Couette Flow; Nonlinear Extension of Syngeโs Theorem -- ยง 41. The Optimum Energy Stability Boundary for Axisymmetric Disturbances of Couette Flow -- ยง 42. Comparison of Linear and Energy Limits -- VI. Global Stability of Spiral Couette-Poiseuille Flows -- ยง 43. The Basic Spiral Flow. Spiral Flow Angles -- ยง 44. Eigenvalue Problems of Energy and Linear Theory -- ยง 45. Conditions for the Nonexistence of Subcritical Instability -- ยง 46. Global Stability of Poiseuille Flow between Cylinders which Rotate with the Same Angular Velocity -- ยง 47. Disturbance Equations for Rotating Plane Couette Flow -- ยง 48. The Form of the Disturbance Whose Energy Increases at the Smallest R -- ยง 49. Necessary and Sufficient Conditions for the Global Stability of Rotating Plane Couette Flow -- ยง 50. Rayleighโs Criterion for the Instability of Rotating Plane Couette Flow, Wave Speeds -- ยง 51. The Energy Problem for Rotating Plane Couette Flow when Spiral Disturbances are Assumed from the Start -- ยง 52. Numerical and Experimental Results -- VII. Global Stability of the Flow between Concentric Rotating Spheres -- ยง 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