Instabilities of Flows and Transition to Turbulence

Introduction to Instability and Transition Introduction What Is Instability? Temporal and Spatial Instability Some Instability Mechanisms

Computing Transitional and Turbulent Flows Fluid Dynamical Equations Some Equilibrium Solutions of the Basic Equation Boundary Layer Theory Control Volume Analysis of Boundary Layers Numerical Solution of the Thin Shear Layer (TSL) Equation Laminar Mixing Layer Plane Laminar Jet Issues of Computing Space-Time Dependent Flows Wave Interaction: Group Velocity and Energy Flux Issues of Space-Time Scale Resolution of Flows Temporal Scales in Turbulent Flows Computing Time-Averaged and Unsteady Flows Computing Methods for Unsteady Flows: Dispersion Relation Preserving (DRP) Methods DRP Schemes: Parameter Ranges for Creating q-Waves

Instability and Transition in Flows Introduction Parallel Flow Approximation and Inviscid Instability Theorems Viscous Instability of Parallel Flows Properties of the Orr-Sommerfeld Equation and Boundary Conditions Instability Analysis from the Solution of the Orr-Sommerfeld Equation Receptivity Analysis of the Shear Layer Direct Simulation of Receptivity to Free Stream Excitation Nonparallel and Nonlinear Effects on Instability and Receptivity

Bypass Transition: Theory, Computations and Experiments Introduction Transition via Growing Waves and Bypass Transition Visualization Study of Vortex-Induced Instability as Bypass Transition Computations of Vortex-Induced Instability as a Precursor to Bypass Transition The Instability Mechanism in Vortex-Induced Instability Instability at the Attachment Line of Swept Wings

Spatio-Temporal Wave Front and Transition Introduction Transient Energy Growth Bromwich Contour Integral Method and Energy-Based Receptivity Analysis Spatio-Temporal Wave Front Obtained by the Bromwich Contour Integral Method Nonlinear Receptivity Analysis: Transition by the Spatio-Temporal Front and Bypass Route Calculation of the N Factor

Nonlinear Effects: Multiple Hopf Bifurcations and Proper Orthogonal Decomposition Introduction Receptivity of Bluff-Body Flows to Background Disturbances Multiple Hopf Bifurcations, Landau Equation and Flow Instability Instability of Flow Past a Cylinder Role of FST on Critical Reynolds Number for a Cylinder POD Modes and Nonlinear Stability The Landau-Stuart-Eckhaus Equation Universality of POD Modes

Stability and Transition of Mixed Convection Flows Introduction The Governing Equations Equilibrium Boundary Layer Flow Equations Linear Spatial Stability Analysis of the Boundary Layer over a Heated Plate Nonlinear Receptivity of Mixed Convection Flow over a Heated Plate Concluding Remarks

Instabilities of Three-Dimensional Flows Introduction Three-Dimensional Flows Infinite Swept Wing Flow Attachment Line Flow Boundary Layer Equations in the Transformed Plane Simplification of Boundary Layer Equations in the Transformed Plane Instability of Three-Dimensional Flows Linear Stability Theory for Three-Dimensional Flows Experimental Evidence of Instability on Swept Wings Infinite Swept Wing Boundary Layer Stability of the Falkner-Skan-Cooke Profile Stationary Waves over Swept Geometries Traveling Waves over Swept Geometries Attachment Line Problem Empirical Transition Prediction Method for Three-Dimensional Flows

Analysis and Design of Natural Laminar Flow Airfoils Introduction Airfoil Nomenclature and Basic Aerodynamic Properties Pressure Distribution and Pressure Recovery of Some Low Drag Airfoils Flapping of Airfoils Effects of Roughness and Fixing Transition Effects of Vortex Generator or Boundary Layer Re-energizer Section Characteristics of Various Profiles High Speed NLF Airfoils Direct Simulation of Bypass Transitional Flow Past an Airfoil

Epilogue Introduction Relevance of Two-Dimensional Turbulence Role of Formulation in the Numerical Solution in Two-dimensional DNS Dynamical System Representation of Turbulent Flows Role of the Computational Domain Free and Forced Turbulence

Selected Problems Bibliography and Index