The Israel-Palestine Conflict A History,9780387989853

The Israel-Palestine Conflict A History

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Edition: 4th
ISBN13: 9780387989853
ISBN10: 0387989854
Format: Paperback
Pub. Date: 2021-06-01
Publisher(s): Cambridge
List Price: $359.98

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Summary

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.

Table of Contents

Preface xi
Introduction and General Results
1(14)
Introduction
1(1)
Nonlinear Disturbance Equations
2(1)
Definition of Stability and Critical Reynolds Numbers
3(4)
Definition of Stability
3(2)
Critical Reynolds Numbers
5(1)
Spatial Evolution of Disturbances
6(1)
The Reynolds-Orr Equation
7(8)
Derivation of the Reynolds-Orr Equation
7(2)
The Need for Linear Growth Mechanisms
9(6)
I Temporal Stability of Parallel Shear Flows
Linear Inviscid Analysis
15(40)
Inviscid Linear Stability Equations
15(2)
Modal Solutions
17(21)
General Results
17(16)
Dispersive Effects and Wave Packets
33(5)
Initial Value Problem
38(17)
The Inviscid Initial Value Problem
38(4)
Laplace Transform Solution
42(4)
Solutions to the Normal Vorticity Equation
46(2)
Example: Couette Flow
48(2)
Localized Disturbances
50(5)
Eigensolutions to the Viscous Problem
55(44)
Viscous Linear Stability Equations
55(9)
The Velocity-Vorticity Formulation
55(1)
The Orr-Sommerfeld and Squire Equations
56(2)
Squire's Transformation and Squire's Theorem
58(1)
Vector Modes
59(2)
Pipe Flow
61(3)
Spectra and Eigenfunctions
64(21)
Discrete Spectrum
64(7)
Neutral Curves
71(3)
Continuous Spectrum
74(4)
Asymptotic Results
78(7)
Further Results on Spectra and Eigenfunctions
85(14)
Adjoint Problem and Bi-Orthogonality Condition
85(4)
Sensitivity of Eigenvalues
89(4)
Pseudo-Eigenvalues
93(1)
Bounds on Eigenvalues
94(2)
Dispersive Effects and Wave Packets
96(3)
The Viscous Initial Value Problem
99(54)
The Viscous Initial Value Problem
99(4)
Motivation
99(3)
Derivation of the Disturbance Equations
102(1)
Disturbance Measure
102(1)
The Forced Squire Equation and Transient Growth
103(3)
Eigenfunction Expansion
103(2)
Blasius Boundary Layer Flow
105(1)
The Complete Solution to the Initial Value Problem
106(5)
Continuous Formulation
106(2)
Discrete Formulation
108(3)
Optimal Growth
111(15)
The Matrix Exponential
111(1)
Maximum Amplification
112(7)
Optimal Disturbances
119(1)
Reynolds Number Dependence of Optimal Growth
120(6)
Optimal Response and Optimal Growth Rate
126(13)
The Forced Problem and the Resolvent
126(5)
Maximum Growth Rate
131(2)
Response to Stochastic Excitation
133(6)
Estimates of Growth
139(5)
Bounds on Matrix Exponential
139(2)
Conditions for No Growth
141(3)
Localized Disturbances
144(9)
Choice of Initial Disturbances
144(3)
Examples
147(2)
Asymptotic Behavior
149(4)
Nonlinear Stability
153(44)
Motivation
153(2)
Introduction
153(1)
A Model Problem
154(1)
Nonlinear Initial Value Problem
155(5)
The Velocity-Vorticity Equations
155(5)
Weakly Nonlinear Expansion
160(7)
Multiple-Scale Analysis
160(4)
The Landau Equation
164(3)
Three-Wave Interactions
167(10)
Resonance Conditions
167(1)
Derivation of a Dynamical System
168(4)
Triad Interactions
172(5)
Solutions to the Nonlinear Initial Value Problem
177(11)
Formal Solutions to the Nonlinear Initial Value Problem
177(2)
Weakly Nonlinear Solutions and the Center Manifold
179(1)
Nonlinear Equilibrium States
180(5)
Numerical Solutions for Localized Disturbances
185(3)
Energy Theory
188(9)
The Energy Stability Problem
188(3)
Additional Constraints
191(6)
II Stability of Complex Flows and Transition
Temporal Stability of Complex Flows
197(56)
Effect of Pressure Gradient and Crossflow
198(9)
Falkner-Skan (FS) Boundary Layers
198(5)
Falkner-Skan-Cooke (FSC) Boundary layers
203(4)
Effect of Rotation and Curvature
207(9)
Curved Channel Flow
207(4)
Rotating Channel Flow
211(2)
Combined Effect of Curvature and Rotation
213(3)
Effect of Surface Tension
216(7)
Water Table Flow
216(2)
Energy and the Choice of Norm
218(3)
Results
221(2)
Stability of Unsteady Flow
223(14)
Oscillatory Flow
223(6)
Arbitrary Time Dependence
229(8)
Effect of Compressibility
237(16)
The Compressible Initial Value Problem
237(3)
Inviscid Instabilities and Rayleigh's Criterion
240(6)
Viscous Instability
246(3)
Nonmodal Growth
249(4)
Growth of Disturbances in Space
253(120)
Spatial Eigenvalue Analysis
253(17)
Introduction
253(2)
Spatial Spectra
255(9)
Gaster's Transformation
264(2)
Harmonic Point Source
266(4)
Absolute Instability
270(20)
The Concept of Absolute Instability
270(3)
Briggs' Method
273(5)
The Cusp Map
278(3)
Stability of a Two-Dimensional Wake
281(3)
Stability of Rotating Disk Flow
284(6)
Spatial Initial Value Problem
290(10)
Primitive Variable Formulation
290(1)
Solution of the Spatial Initial Value Problem
291(3)
The Vibrating Ribbon Problem
294(6)
Nonparallel Effects
300(44)
Asymptotic Methods
301(8)
Parabolic Equations for Steady Disturbances
309(9)
Parabolized Stability Equations (PSE)
318(11)
Spatial Optimal Disturbances
329(8)
Global Instability
337(7)
Nonlinear Effects
344(7)
Nonlinear Wave Interactions
344(2)
Nonlinear Parabolized Stability Equations
346(3)
Examples
349(2)
Disturbance Environment and Receptivity
351(22)
Introduction
351(2)
Nonlocalized and Localized Receptivity
353(10)
An Adjoint Approach to Receptivity
363(4)
Receptivity Using Parabolic Evolution Equations
367(6)
Secondary Instability
373(28)
Introduction
373(1)
Secondary Instability of Two-Dimensional Waves
374(9)
Derivation of the Equations
374(4)
Numerical Results
378(3)
Elliptical Instability
381(2)
Secondary Instability of Vortices and Streaks
383(11)
Governing Equations
383(6)
Examples of Secondary Instability of Streaks and Vortices
389(5)
Eckhaus Instability
394(7)
Secondary Instability of Parallel Flows
394(3)
Parabolic Equations for Spatial Eckhaus Instability
397(4)
Transition to Turbulence
401(128)
Transition Scenarios and Thresholds
401(13)
Introduction
401(2)
Three Transition Scenarios
403(8)
The Most Likely Transition Scenario
411(2)
Conclusions
413(1)
Breakdown of Two-Dimensional Waves
414(11)
The Zero Pressure Gradient Boundary Layer
414(6)
Breakdown of Mixing Layers
420(5)
Streak Breakdown
425(11)
Streaks Forced by Blowing or Suction
425(4)
Freestream Turbulence
429(7)
Oblique Transition
436(10)
Experiments and Simulations in Blasius Flow
436(5)
Transition in a Separation Bubble
441(4)
Compressible Oblique Transition
445(1)
Transition of Vortex-Dominated Flows
446(10)
Transition in Flows with Curvature
446(4)
Direct Numerical Simulations of Secondary Instability of Crossflow Vortices
450(5)
Experimental Investigations of Breakdown of Cross-flow Vortices
455(1)
Breakdown of Localized Disturbances
456(9)
Experimental Results for Boundary Layers
459(1)
Direct Numerical Simulations in Boundary Layers
460(5)
Transition Modeling
465(14)
Low-Dimensional Models of Subcritical Transition
465(4)
Traditional Transition Prediction Models
469(2)
Transition Prediction Models Based on Nonmodal Growth
471(3)
Nonlinear Transition Modeling
474(5)
III Appendix
A Numerical Issues and Computer Programs
479(30)
A.1 Global versus Local Methods
479(1)
A.2 Runge-Kutta Methods
480(3)
A.3 Chebyshev Expansions
483(3)
A.4 Infinite Domain and Continuous Spectrum
486(1)
A.5 Chebyshev Discretization of the Orr-Sommerfeld Equation
487(2)
A.6 MATLAB Codes for Hydrodynamic Stability Calculations
489(14)
A.7 Eigenvalues of Parallel Shear Flows
503(6)
B Resonances and Degeneracies
509(6)
B.1 Resonances and Degeneracies
509(2)
B.2 Orr-Sommerfeld-Squire Resonance
511(4)
C Adjoint of the Linearized Boundary Layer Equation
515(4)
C.1 Adjoint of the Linearized Boundary Layer Equation
515(4)
D Selected Problems on Part I
519(10)
Bibliography 529(22)
Index 551

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