Instability

Question 1

Define stable and unstable flow

Answer 1

Stable if all perturbations which are initially small remain small.

Question 2

Briefly describe linear instability analysis

Answer 2

Denote a basis state with some small perturbation. Neglect non-linear terms.

Denote perturbation as of the form ϕ’ = ϕe^-iωt

Question 3

What do we look for, to identify instability?

Answer 3

The sign of the imaginary portion of the dispersion relation: ω = ωR + i ωI

ω_im > 0 the pertubations grow exp and the solution is unstable.

Question 4

Briefly describe the set up for Rayleigh-Taylor instability

Answer 4

Two fluids of diff density with boundary at z=0. Assume initial velocity and disturbance = 0
Assume outdistance far from interface is zero

Question 5

What boundary conditions do we consider in RT instability?

Answer 5

Dξ/Dt = v1 = v2 at z=ξ
p1 = p2 at z=ξ

As z to +- infty the perturbation velocity = 0