Hydrodynamic stability 2004

Course on Stability and Transition

Reynolds pipe flow experiment

History of shear flow stability and transition

Bypass transition

Disturbance equations

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

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

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 Gmax and Rmax