Notes

Slide Show

Outline

1	Hydrodynamic stability 2004 Part of graduate student course, Department of Mechanics Lectures: 16/9 8-12, K52 30/9 8-12, L44 6/10 8-12, K51 Projects: 10/11 8-12, K52 17/11 8-12, E36 Book: Stability and Transition in Shear Flows Further info on web www2.mech.kth.se/~henning
2	Course on Stability and Transition
3	Reynolds pipe flow experiment
4	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
5	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
6	Disturbance equations
7	Parallel shear flows:
8	Parallel shear flows, cont
9	Orr-Sommerfeld and Squire equations
10	Interpretation of modal results
11	Interpretation of modal results, cont.
12	Squire’s transformation
13	Squire’s theorem
14	Inviscid disturbances
15	Rayleigh’s inflection point criterion
16	Inviscid algebraic instability
17	Lift-up effect
18	Critical Layer
19	Plane Poiseuille flow
20	A, P, S- Eigenfunctions for PPF
21	Blasius boundary layer
22	Continuous spectrum
23	Critical Reynolds numbers
24	The intial value problem (IVP)
25	A simple eigenfunction expansion
26	Transient growth
27	Model with non-orthogonal eigenfunctions
28	General formulation of viscous IVP
29	Disturbance measure
30	Adjoint OS-SQ system
31	Biorthogonality
32	Component form of adjoint
33	Solution of IVP using eigenfunction expansions
34	Discrete formulation
35	Discrete formulation, cont.
36	Maximum amplification
37	2D PPF: envelope and selected IC
38	2D PPF: dependence on N
39	3D PPF and Blasius flow, Re=1000
40	Optimal disturbances PPF, Re=1000
41	The forced problem and the resolvent
42	Discrete formulation
43	Maximum response to forcing
44	Pseudospectra, resolvents and sensitivity
45	PPF: resolvents, growth and forcing
46	PPF: resolvents, growth and forcing
47	Re-dependence of growth and response
48	Re-dependence, cont.
49	Re-dependence of Gmax for PPF
50	Re-dependence of Gmax and Rmax