Introduction to Instability and Transition – 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 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 – Receptivity by Linearized Approach: Connection to Stability Theory – Receptivity to Wall Excitation and Impulse Response – Vibrating Ribbon at the Wall – Receptivity to Free Stream Excitation – General Excitation and Upstream Propagating Modes – Low Frequency Free Stream Excitation and the Klebanoff Mode – Direct Simulation of Receptivity to Free Stream Excitation – Nonparallel and Nonlinear Effects on Instability and Receptivity – Bypass Transition: Theory, Computations, and Experiments – Spatio-Temporal Wave Front and Transition – Nonlinear Effects: Multiple Hopf Bifurcations and Proper Orthogonal Decomposition – Stability and Transition of Mixed Convection Flows – Instabilities of Three-Dimensional Flows – Analysis and Design of Natural Laminar Flow Airfoils

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