Anteckningar
Disposition
Course on Stability and Transition
Reynolds pipe flow experiment
History of shear flow stability and transition
Reynolds pipe flow experiment (1883)
Rayleigh’s inflection point criterion (1887)
Orr (1907) Sommerfeld (1908) viscous eq.
Heisenberg (1924) viscous channel solution
Tollmien (1931) Schlichting (1933) viscous BL solution
Schubauer & Skramstad (1947) experimental TS-wave verification
Klebanoff, Tidstrom & Sargent (1962) 3D breakdown
Bypass transition
High and low speed streaks in the streamwise direction
Transition due to free-stream turbulence
Klebanoff (1977) modes,    Tu > 0.5% in BL
Subcritical transition in Poiseuille and Couette flows
Disturbance equations
Stability definitions
Stability definitions
Critical Reynolds numbers
Critical Reynolds numbers
Reynolds-Orr equation
Linear growth mechanisms
Evolution of disturbances in shear flows
Parallel shear flows:
Parallel shear flows, cont
Orr-Sommerfeld and Squire equations
Interpretation of modal results
Interpretation of modal results, cont.
Squire’s transformation
Squire’s theorem
Inviscid disturbances
Rayleigh’s inflection point criterion
Inviscid algebraic instability
Lift-up effect
Critical Layer
Thickness of critical layer
Plane Poiseuille flow
A, P, S- Eigenfunctions for PPF
Blasius boundary layer
Continuous spectrum
Critical Reynolds numbers
The intial value problem (IVP)
A simple eigenfunction expansion
Transient growth
Model with non-orthogonal eigenfunctions
General formulation of viscous IVP
Disturbance measure
Adjoint OS-SQ system
Biorthogonality
Component form of adjoint
Solution of IVP using eigenfunction expansions
Discrete formulation
Discrete formulation, cont.
Maximum amplification
2D PPF: envelope and selected IC
2D PPF: dependence on N
3D PPF and Blasius flow, Re=1000
3D PPF: G(t), Re=1000
Optimal disturbances PPF, Re=1000
The forced problem and the resolvent
Discrete formulation
Maximum response to forcing
Pseudospectra, resolvents and sensitivity
PPF: resolvents, growth and forcing
PPF: resolvents, growth and forcing
Re-dependence of growth and response
Re-dependence, cont.
Re-dependence of Gmax for PPF
Re-dependence of Rmax for PCF
Re-dependence of Gmax and Rmax