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Symbol Description | p. ix |
List of Figures | p. xv |
List of Tables | p. xxvii |
Preface | p. xxix |
Introduction to Instability and Transition | p. 1 |
Introduction | p. 1 |
What Is Instability? | p. 4 |
Temporal and Spatial Instability | p. 4 |
Some Instability Mechanisms | p. 5 |
Dynamic Stability of Still Atmosphere | p. 5 |
Kelvin-Helmholtz Instability | p. 7 |
Computing Transitional and Turbulent Flows | p. 11 |
Fluid Dynamical Equations | p. 11 |
Equation of Continuity | p. 12 |
Momentum Conservation Equation | p. 12 |
Energy Conservation Equation | p. 14 |
Alternate Forms of the Energy Equation | p. 15 |
Equations of Motion in Terms of Derived Variables | p. 15 |
Some Equilibrium Solutions of the Basic Equation | p. 16 |
Couette Flow between Parallel Plates | p. 18 |
Flow between Concentric Rotating Cylinders | p. 19 |
Couette Flow between Parallel Plates, Driven by Pressure | p. 21 |
Steady Stagnation Point Flow | p. 24 |
Flow Past a Rotating Disc | p. 26 |
Boundary Layer Theory | p. 30 |
Control Volume Analysis of Boundary Layers | p. 35 |
Displacement Thickness | p. 36 |
Momentum Thickness | p. 36 |
Separation of a Steady Boundary Layer | p. 37 |
Accelerated Flows (dp/dx < 0) | p. 38 |
Retarded Flow (dp/dx > 0) | p. 38 |
Numerical Solution of the Thin Shear Layer (TSL) Equation | p. 40 |
Falkner-Skan Similarity Profile | p. 43 |
Separation Criterion for Wedge Flow | p. 44 |
Blasius Profile | p. 44 |
Hiemenz or Stagnation Point Flow | p. 44 |
Laminar Mixing Layer | p. 44 |
Plane Laminar Jet | p. 46 |
Issues of Computing Space-Time Dependent Flows | p. 48 |
Waves - Building Blocks of a Disturbance Field | p. 49 |
Plane Waves | p. 50 |
Wave Interaction: Group Velocity and Energy Flux | p. 51 |
Physical and Computational Implications of Group Velocity | p. 52 |
Wave Packets and Their Propagation | p. 53 |
Issues of Space-Time Scale Resolution of Flows | p. 54 |
Spatial Scales in Turbulent Flows | p. 54 |
Two- and Three-Dimensional DNS | p. 55 |
Temporal Scales in Turbulent Flows | p. 57 |
Computing Time-Averaged and Unsteady Flows | p. 59 |
Computing Methods for Unsteady Flows: Dispersion Relation Preserving (DRP) Methods | p. 61 |
Spectral or Numerical Amplification Factor | p. 62 |
Quantification of Dispersion Error | p. 65 |
DRP Schemes: Parameter Ranges for Creating q-Waves | p. 68 |
Instability and Transition in Flows | p. 75 |
Introduction | p. 75 |
Parallel Flow Approximation and Inviscid Instability Theorems | p. 76 |
Inviscid Instability Mechanism | p. 78 |
Viscous Instability of Parallel Flows | p. 79 |
Eigenvalue Formulation for Instability of Parallel Flows | p. 80 |
Temporal and Spatial Amplification of Disturbances | p. 83 |
Temporal Amplification Theory | p. 83 |
Spatial Amplification Theory | p. 83 |
Relationship between Temporal and Spatial Theories | p. 84 |
Properties of the Orr-Sommerfeld Equation and Boundary Conditions | p. 85 |
Compound Matrix Method | p. 87 |
Instability Analysis from the Solution of the Orr-Sommerfeld Equation | p. 91 |
Local and Total Amplification of Disturbances | p. 95 |
Effects of the Mean Flow Pressure Gradient | p. 97 |
Transition Prediction Based on Stability Calculation | p. 102 |
Effects of Free Stream Turbulence | p. 103 |
Receptivity Analysis of the Shear Layer | p. 106 |
Receptivity Mechanism by a Linearized Approach: Connection to Stability Theory | p. 107 |
A Brief Review of Laplace-Fourier Transforms | p. 107 |
Fourier and Laplace Transforms | p. 108 |
Inversion Formula for Laplace Transforms | p. 110 |
A Short Tutorial on Fourier Integral and Transforms | p. 112 |
Some Useful Laplace-Fourier Transforms | p. 115 |
Receptivity to Wall Excitation and Impulse Response | p. 118 |
Near-Field Response Created by Localized Excitation | p. 120 |
Outer Solution | p. 122 |
Inner Solution | p. 122 |
Vibrating Ribbon at the Wall | p. 127 |
Receptivity to Free Stream Excitation | p. 130 |
General Excitation and Upstream Propagating Modes | p. 132 |
Low Frequency Free Stream Excitation and the Klebanoff Mode | p. 138 |
Direct Simulation of Receptivity to Free Stream Excitation | p. 140 |
Coupling between the Wall and Free Stream Modes | p. 144 |
Receptivity to a Train of Convected Vortices in the Free Stream | p. 147 |
Further Explanation of Free Stream Periodic Excitation | p. 151 |
Nonparallel and Nonlinear Effects on Instability and Receptivity | p. 155 |
Time Varying Receptivity Problem vis-a-vis the Signal Problem | p. 158 |
Evidence of Nonparallel and Nonlinear Effects | p. 159 |
Limitations of Linearized Nonparallel Theories | p. 166 |
Bypass Transition: Theory, Computations, and Experiments | p. 171 |
Introduction | p. 171 |
Transition via Growing Waves and Bypass Transition | p. 177 |
Visualization Study of Vortex-Induced Instability as Bypass Transition | p. 179 |
Computations of Vortex-Induced Instability as a Precursor to Bypass Transition | p. 189 |
Instability Mechanism in Vortex-Induced Instability | p. 192 |
Instability at the Attachment Line of Swept Wings | p. 195 |
Spatio-Temporal Wave Front and Transition | p. 201 |
Introduction | p. 201 |
Transient Energy Growth | p. 205 |
Bromwich Contour Integral Method and Energy-Based Receptivity Analysis | p. 206 |
Spatio-Temporal Wave Front Obtained by the Bromwich Contour Integral Method | p. 207 |
Nonlinear Receptivity Analysis: Transition by the Spatio-Temporal Front and Bypass Route | p. 217 |
Governing Equations and Boundary Condition | p. 219 |
Nonlinear Receptivity to Vortical Wall Excitation | p. 223 |
Low Amplitude, Moderate Frequency Excitation | p. 226 |
High Amplitude Cases and Spot Regeneration Mechanism | p. 229 |
Low Frequency Excitation Cases: Different Route of Transition | p. 234 |
Calculation of the N Factor | p. 240 |
Nonlinear Effects: Multiple Hopf Bifurcations and Proper Orthogonal Decomposition | p. 245 |
Introduction | p. 245 |
Receptivity of Bluff-Body Flows to Background Disturbances | p. 246 |
Numerical Simulation of Flow Past a Cylinder | p. 251 |
Multiple Hopf Bifurcations, Landau Equation and Flow Instability | p. 256 |
Instability of Flow Past a Cylinder | p. 258 |
Role of FST on Critical Reynolds Number for a Cylinder | p. 260 |
POD Modes and Nonlinear Stability | p. 263 |
Landau-Stuart-Eckhaus Equation | p. 274 |
Universality of POD Modes | p. 276 |
Stability and Transition of Mixed Convection Flows | p. 293 |
Introduction | p. 293 |
Governing Equations | p. 297 |
Equilibrium Boundary Layer Flow Equations | p. 298 |
Schneider's Similarity Solution | p. 299 |
Linear Spatial Stability Analysis of the Boundary Layer over a Heated Plate | p. 305 |
Fundamental Solutions of the OSE | p. 310 |
Compound Matrix Method for the Sixth Order OSE | p. 312 |
Initial Conditions for an Auxiliary System of Equations | p. 315 |
Dispersion Relation | p. 316 |
The Grid Search Method and the Newton-Raphson Technique for Obtaining Eigenspectrum | p. 316 |
Neutral Curve and Wavenumber Contours | p. 319 |
Precision in Computing | p. 321 |
Results of the Linear Spatial Stability Theory | p. 322 |
Nonlinear Receptivity of Mixed Convection Flow over a Heated Plate | p. 333 |
Boundary and Initial Conditions | p. 336 |
Eigenfunction Structure and DNS of the Mixed Convection Problem | p. 356 |
Concluding Remarks | p. 358 |
Instabilities of Three-Dimensional Flows | p. 361 |
Introduction | p. 361 |
Three-Dimensional Flows | p. 361 |
Infinite Swept Wing Flow | p. 364 |
Attachment Line Flow | p. 365 |
Boundary Layer Equations in the Transformed Plane | p. 367 |
Simplification of Boundary Layer Equations in the Transformed Plane | p. 368 |
Instability of Three-Dimensional Flows | p. 369 |
Effects of Sweep Back and Cross Flow Instability | p. 370 |
Linear Stability Theory for Three-Dimensional Flows | p. 372 |
Temporal Instability of Three-Dimensional Flows | p. 373 |
Spatial Instability of Three-Dimensional Flows | p. 374 |
Experimental Evidence of Instability on Swept Wings | p. 376 |
Infinite Swept Wing Boundary Layer | p. 377 |
Stability of the Falkner-Skan-Cooke Profile | p. 381 |
Stationary Waves over Swept Geometries | p. 384 |
Traveling Waves over Swept Geometries | p. 386 |
Attachment Line Problem | p. 387 |
Empirical Transition Prediction Method for Three-Dimensional Flows | p. 389 |
Streamwise Transition Criterion | p. 389 |
Cross Flow Transition Criteria | p. 389 |
Leading Edge Contamination Criterion | p. 390 |
Analysis and Design of Natural Laminar Flow Airfoils | p. 393 |
Introduction | p. 393 |
Airfoil Nomenclature and Basic Aerodynamic Properties | p. 394 |
Pressure Distribution and Pressure Recovery of Some Low Drag Airfoils | p. 402 |
Flapping of Airfoils | p. 406 |
Effects of Roughness and Fixing Transition | p. 407 |
Effects of Vortex Generator or Boundary Layer Re-Energizer | p. 409 |
Section Characteristics of Various Profiles | p. 410 |
High Speed NLF Airfoils | p. 412 |
Direct Simulation of Bypass Transitional Flow Past an Airfoil | p. 420 |
Epilogue | p. 425 |
Introduction | p. 425 |
Relevance of Two-Dimensional Turbulence | p. 426 |
Role of Formulation in the Numerical Solution in Two-Dimensional DNS | p. 427 |
Dynamical System Representation of Turbulent Flows | p. 429 |
Role of the Computational Domain | p. 431 |
Renewal Mechanism and Intermittent Nature of Turbulence | p. 433 |
Free and Forced Turbulence | p. 437 |
Selected Problems | p. 441 |
Bibliography | p. 447 |
Index | p. 473 |
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