Nonlinear Interactions and Transition

Non-linear disturbance equations

Stability definitions

Critical Reynolds numbers

Reynolds-Orr equation

Linear growth mechanisms

Quadratic non-linear interactions

Non-linear v-eta formulation

Fourier-transformed equations

Convolution sums and triad interactions

Example

Rate of change of energy

Conservation of energy in triads

Non-linear equilibrium states

2D finite amplitude states in PPF

Secondary instability of 2D waves

Form of the solution

Classification of modes

Secondary instability equations

Secondary instability of 2D TS waves

Transition to turbulence: 3 scenarios

2^nd instability of TS-waves

Streak breakdown

Oblique transition

Transition times vs disturbance energy

Threshold for transition in PPF

DNS of 2^nd breakdown of TS-waves

Free-stream turbulence and streak breakdown

Klebanoff mode and optimal growth

DNS of oblique transition

DNS of Wiegel experiment

Transition types in Wiegel experiment

Secondary instability of cross-flow vortices

Lerche experiment of CF-vortices