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Book
xx, 605 p. : ill. ; 23 cm.
  • Foreword-- Preface-- 1. Introduction-- 2. Thermal instability-- 3. Centrifugal instability-- 4. Parallel shear flows-- 5. Uniform asymptotic approximations-- 6. Additional topics in linear stability theory-- 7. Nonlinear stability-- Appendix A. A class of generalized Airy functions-- Appendix B. Solutions to the problems-- Bibliography-- Motion picture index-- Subject index.
  • (source: Nielsen Book Data)9780521525411 20160528
Hydrodynamic stability is of fundamental importance in fluid mechanics and is concerned with the problem of transition from laminar to turbulent flow. Drazin and Reid emphasise throughout the ideas involved, the physical mechanisms, the methods used, and the results obtained, and, wherever possible, relate the theory to both experimental and numerical results. A distinctive feature of the book is the large number of problems it contains. These problems not only provide exercises for students but also provide many additional results in a concise form. This new edition of this celebrated introduction differs principally by the inclusion of detailed solutions for those exercises, and by the addition of a Foreword by Professor J. W. Miles.
(source: Nielsen Book Data)9780521525411 20160528
Engineering Library (Terman), eReserve
ME-451B-01
Book
xxii, 441 p. : ill. ; 24 cm.
  • 1. Introduction and problem formulation-- 2. Temporal stability of inviscid incompressible flows-- 3. Temporal stability of viscous incompressible flows-- 4. Spatial stability of incompressible flows-- 5. Stability of compressible flows-- 6. Centrifugal stability-- 7. Geophysical flow-- 8. Transient dynamics-- 9. Nonlinear stability-- 10. Transition and receptivity-- 11. Direct numerical simulation-- 12. Flow control and optimization-- 13. Investigating hydrodynamic instabilities with experiments-- Bibliography-- Index.
  • (source: Nielsen Book Data)9780521632003 20160528
The study of hydrodynamic stability is fundamental to many subjects, ranging from geophysics and meteorology through to engineering design. This treatise covers both classical and modern aspects of the subject, systematically developing it from the simplest physical problems, then progressing chapter by chapter to the most complex, considering linear and nonlinear situations, and analysing temporal and spatial stability. The authors examine each problem both analytically and numerically: many chapters end with an appendix outlining relevant numerical techniques. All relevant fluid flows are treated, including those where the fluid may be compressible, or those from geophysics, or those that require salient geometries for description. Details of initial-value problems are explored equally with those of stability. As a result, the early transient period as well as the asymptotic fate for perturbations for a flow can be assessed. The text is enriched with many exercises, copious illustrations and an extensive bibliography and the result is a book that can be used with courses on hydrodynamic stability or as an authoritative reference for researchers.
(source: Nielsen Book Data)9780521632003 20160528
Engineering Library (Terman), eReserve
ME-451B-01
Book
xiii, 556 p. : ill. ; 25 cm.
  • Introduction.- General results.- Linear inviscid analysis.- Eigensolutions to the viscous problem.- Linear transient growth.- Non-linear results.- The spatial problem.- Appendix A. Notes on numerical methods for accurate results.- Appendix B. Model problem.
  • (source: Nielsen Book Data)9780387989853 20160528
This book is a detailed look at some of the more modern issues of hydrodynamic stability, including transient growth, eigenvalue spectra, secondary instability. Analytical results and numerical simulations, linear and (selected) nonlinear stability methods will be presented. By including classical results as well as recent developments in the field of hydrodynamic stability and transition, the book can be used as a textbook for an introductory, graduate-level course in stability theory or for a special-topics fluids course. It will also be of value as a reference for researchers in the field of hydrodynamic stability theory or with an interest in recent developments in fluid dynamics. Since the appearance of "Drazin & Reid", no book on hydrodynamic stability theory has been published. However, stability theory has seen a rapid development over the past decade. Direct numerical simulations of transition to turbulence and linear analysis based on the initial-value problem are two of many such developments that will be included in the book.
(source: Nielsen Book Data)9780387989853 20160528
Engineering Library (Terman)
ME-451B-01
Book
xiv, 525 p. : ill. ; 22 cm.
  • Preface-- 1. Introduction-- 2. Thermal instability-- 3. Centrifugal instability-- 4. Parallel shear flows-- 5. Uniform asymptotic approximations-- 6. Additional topics in linear stability theory-- 7. Nonlinear stability-- Appendix-- Bibliography and indexes.
  • (source: Nielsen Book Data)9780521227988 20160528
Hydrodynamic stability is of fundamental importance in fluid mechanics and is concerned with the problem of transition from laminar to turbulent flow. This book begins with a basic introduction to three major areas of the subject: thermal convection, rotating and curved flows, and parallel shear flows. There follows a comprehensive account of recent advances in the mathematical theory for parallel shear flows. A number of applications of the linear theory are discussed, including the effects of stratification and unsteadiness. The book concludes with a chapter describing some of the fundamental ideas involved in current work on nonlinear hydrodynamic stability. The emphasis throughout is on the ideas involved, the physical mechanisms, the methods used, and the results obtained, and, wherever possible, the theory is related to both experimental and numerical results. A distinctive feature of the book is the large number of problems it contains. These problems, for which hints and references are given, not only provide exercises for students but also provide many additional results in a concise form.
(source: Nielsen Book Data)9780521227988 20160528
Engineering Library (Terman)
ME-451B-01
Book
2 v. : ill. ; 25 cm.
Green Library, Engineering Library (Terman), SAL3 (off-campus storage)
ME-451B-01
Book
1 online resource (volumes)
  • 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.- (a) The Reynolds Number.- (b) Bibliographical Notes.- 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.- (a) Parabolic Poiseuille Flow.- (b) Poiseuille Flow in an Annular Pipe.- 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 and Response 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.- (a) The Spectral Problem.- (b) The Perturbation Series.- (c) Some Properties of the Bifurcating Solution.- 35. Comparison of Theory and Experiment.- (a) Instability of Laminar Poiseuille Flow.- (b) Description of the Diagrams.- (c) Inferences and Conjectures.- 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 Rotating Plane 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.- (a) Basic Flow.- (b) Stability Analysis.- (c) Experimental and Numerical Results.- 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.
  • (source: Nielsen Book Data)9783642809934 20160619
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 theory which I regard as established. Acknowledgements I started writing this book in 1967 at the invitation of Clifford Truesdell. It was to be a short work on the energy theory of stability and if I had stuck to that I would have finished the writing many years ago. The theory of stability has developed so rapidly since 1967 that the book I might then have written would now have a much too limited scope. I am grateful to Truesdell, not so much for the invitation to spend endless hours of writing and erasing, but for the generous way he has supported my efforts and encouraged me to higher standards of good work. I have tried to follow Truesdell's advice to write this work in a clear and uncomplicated style. This is not easy advice for a former sociologist to follow; if I have failed it is not due to a lack of urging by him or trying by me. My research during the years 1969-1970 was supported in part by a grant from the Guggenheim foundation to study in London.
(source: Nielsen Book Data)9783642809934 20160619
eReserve
ME-451B-01
Book
1 online resource.
  • VIII. The Oberbeck-Boussinesq Equations. The Stability of Constant Gradient Solutions of the Oberbeck-Boussinesq Equations.- 54. The Oberbeck-Boussinesq Equations for the Basic Flow.- 55. Boundary Conditions.- (a) Temperature Conditions.- (b) Concentration Boundary Conditions.- (c) Velocity Boundary Conditions.- 56. Equations Governing Disturbances of Solutions of the OB Equations.- 57. The ? Family of Energy Equations.- 58. Kinematic Admissibility, Sufficient Conditions for Stability.- 59. Motionless Solutions of the Oberbeck-Boussinesq Equations.- 60. Physical Mechanisms of Instability of the Motionless State.- 61. Necessary and Sufficient Conditions for Stability.- 62. The Benard Problem.- 63. Plane Couette Flow Heated from below.- 64. The Buoyancy Boundary Layer.- IX. Global Stability of Constant Temperature-Gradient and Concentration-Gradient States of a Motionless Heterogeneous Fluid.- 65. Mechanics of the Instability of the Conduction-Diffusion Solutions in a Motionless Heterogeneous Fluid.- 66. Energy Stability of Heated below and Salted above.- 67. Heated and Salted from below: Linear Theory.- 68. Heated and Salted below: Energy Stability Analysis.- 69. Heated and Salted below: Generalized Energy Analysis.- Addendum for Chapter IX: Generalized Energy Theory of Stability for Hydromagnetic Flows.- X. Two-Sided Bifurcation into Convection.- 70. The DOB Equations for Convention of a Fluid in a Container of Porous Material.- 71. The Spectral Problem, the Adjoint Spectral Problem and the Energy Theory of Stability.- 72. Two-Sided Bifurcation.- (a) Simple Eigenvalue.- (b) Multiple Eigenvalues.- (c) Stability of Bifurcating Solutions at Eigenvalues of Higher Multiplicity.- 73. Conditions for the Existence of Two-Sided Bifurcation.- (a) Axisymmetric Convection in Round Containers.- (b) Nonaxisymmetric Convection in Round Containers.- (c) Convection in a Hexagonal Container.- (d) Stability of Solutions Bifurcating at an Eigenvalue of Multiplicity N.- (e) Stability of Bifurcating Hexagonal Convection.- (f) One-Sided Convection in Containers of Rectangular Cross-Section.- (g) The Benard Problem for a DOB Fluid in a Container.- 74. Two-Sided Bifurcation between Spherical Shells.- 75. Stability of the Conduction Solution in a Container Heated below and Internally.- 76. Taylor Series in Two Parameters.- 77. Two-Sided Bifurcation in a Laterally Unbounded Layer of Fluid.- (a) Spectral Crowding.- (b) Cellular Convection.- (c) Stability and the Sign of the Motion in Cellular Convection.- Addendum to Chapter X: Bifurcation Theory for Multiple Eigenvalues.- (a) Membrane Eigenvalues Perturbed by a Nonlinear Term.- (b) Bifurcation from a Simple Eigenvalue.- (c) Bifurcation from a Multiple Eigenvalue.- (d) The Orthogonal Decomposition.- (e) Solvability Conditions.- (f) Perturbation of a Linear Problem at a Double Eigenvalue.- (g) Bifurcation from a Double Eigenvalue: An Example where the Initiating Solvability Condition Occurs at Order l =1 (?1 ? 0).- (h) Bifurcation from a Double Eigenvalue: An Example where the Initiating Solvability Condition Occurs at Order l = 2(?1 = 0, ?2 ? 0).- XI. Stability of Supercritical Convection-Wave Number Selection Through Stability.- 78. Statistically Stationary Convection and Steady Convection.- 79. Stability of Rolls to Noninteracting Three-Dimensional Disturbances.- 80. Nonlinear Neutral Curves for Three-Dimensional Disturbances of Roll Convection.- (a) Oblique-Roll and Cross-Roll Instabilities.- (b) Varicose Instabilities.- (c) Sinuous Instabilities.- 81. Computation of Stability Boundaries by Numerical Methods.- 82. The Amplitude Equation of Newell and Whitehead.- XII. The Variational Theory of Turbulence Applied to Convection in Porous Materials Heated from below.- 83. Bounds on the Heat Transported by Convection.- 84. The Form of the Admissible Solenoidal Fluctuation Field Which Minimizes ? [u, ?-- ?].- 85. Mathematical Properties of the Multi-? Solutions.- 86. The single-? Solution and the Situation for Small ?.- 87. Boundary Layers of the Single-? Solution.- 88. The Two-? Solution.- 89. Boundary-Layers of the Multi-? Solutions.- 90. An Improved Variational Theory Which Makes Use of the Fact that B is Small.- 91. Numerical Computation of the Single-? and Two-? Solution. Remarks about the Asymptotic Limit ? ? ?.- 92. The Heat Transport Curve: Comparison of Theory and Experiment.- XIII. Stability Problems for Viscoelastic Fluids.- 93. Incompressible Simple Fluids. Functional Expansions and Stability.- (a) Functional Expansions of ?, Stability and Bifurcation.- (b) Generation of the History of a Motion.- (c) Stability and Bifurcation of Steady Flow.- 94. Stability and Bifurcation of the Rest State.- (a) Slow Motion.- (b) Time-Dependent Perturbations of the Rest State.- (c) Stability of the Rest State.- (d) Bifurcation of the Rest State of a Simple Fluid Heated from below.- 95. Stability of Motions of a Viscoelastic Fluid.- (a) The Climbing Fluid Instability.- (b) Symmetry Breaking Instabilities of the Time-Periodic Motion Induced by Torsional Oscillations of a Rod.- (c) The Striping Instability.- (d) Tall Taylor Cells in Polyacrylamide.- XIV. Interfacial Stability.- 96. The Mechanical Energy Equation for the Two Fluid System.- 97. Stability of the Interface between Motionless Fluids When the Contact Line is Fixed.- 98. Stability of a Column of Liquid Resting on a Column of Air in a Vertical Tube-Static Analysis.- 99. Stability of a Column of Liquid Resting on a Column of Air in a Vertical Tube-Dynamic Analysis.- Notes for Chapter XIV.- References.
  • (source: Nielsen Book Data)9783642809965 20170418
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 theory which I regard as established. Acknowledgements I started writing this book in 1967 at the invitation of Clifford Truesdell. It was to be a short work on the energy theory of stability and if I had stuck to that I would have finished the writing many years ago. The theory of stability has developed so rapidly since 1967 that the book I might then have written would now have a much too limited scope. I am grateful to Truesdell, not so much for the invitation to spend endless hours of writing and erasing, but for the generous way he has supported my efforts and encouraged me to higher standards of good work. I have tried to follow Truesdell's advice to write this work in a clear and uncomplicated style. This is not easy advice for a former sociologist to follow; if I have failed it is not due to a lack of urging by him or trying by me. My research during the years 1969-1970 was supported in part by a grant from the Guggenheim foundation to study in London.
(source: Nielsen Book Data)9783642809965 20170418
Engineering Library (Terman)
ME-451B-01