Stability and Transition in Shear Flows

1 Introduction and General Results.- 1.1 Introduction.- 1.2 Nonlinear Disturbance Equations.- 1.3 Definition of Stability and Critical Reynolds Numbers.- 1.4 The Reynolds-Orr Equation.- I Temporal Stability of Parallel Shear Flows.- 2 Linear Inviscid Analysis.- 3 Eigensolutions to the Viscous Problem.- 4 The Viscous Initial Value Problem.- 5 Nonlinear Stability.- II Stability of Complex Flows and Transition.- 6 Temporal Stability of Complex Flows.- 7 Growth of Disturbances in Space.- 8 Secondary Instability.- 9 Transition to Turbulence.- III Appendix.- A Numerical Issues and Computer Programs.- A.1 Global versus Local Methods.- A.2 Runge-Kutta Methods.- A.3 Chebyshev Expansions.- A.4 Infinite Domain and Continuous Spectrum.- A.5 Chebyshev Discretization of the Orr-Sommerfeld Equation.- A.6 MATLAB Codes for Hydrodynamic Stability Calculations.- A.7 Eigenvalues of Parallel Shear Flows.- B Resonances and Degeneracies.- B.1 Resonances and Degeneracies.- B.2 Orr-Sommerfeld-Squire Resonance.- C Adjoint of the Linearized Boundary Layer Equation.- C.1 Adjoint of the Linearized Boundary Layer Equation.- D Selected Problems on Part I.