Week 3 - Instabilities

Question 1

What is the Rayleigh criterion for instability?

Answer 1

dJ^2/dR < 0

Question 2

How does the Rayleigh-Taylor instability emerge? And what is the difference between this and the Kelvin-Helmholtz instability?

Answer 2

When two fluids of different density intersect and the lighter fluid pushes the heavier one. (Mushroom cloud)

Kelvin-Helmholtz instability is the opposite: the heavier fluid pushes the lighter one, i.e. the heavier lies below the lighter. (Waves)

Question 3

What is the difference between a marginally stable and a metastable system?

Answer 3

The marginally stable system is in saddle point while the metastable is next to a bump

Question 4

What is Couette flow?

Answer 4

The flow of a viscous fluid between two tangential surfaces with some relative motion.

Question 5

How can we evaluate if interstellar gas is rotationally stable?

Answer 5

By looking at the rotation curve

Question 6

What instability is said to be buoyancy-driven?

Answer 6

Rayleigh-Taylor instability

Question 7

What instability is said to be shear-driven?

Answer 7

Kelvin-Helmholtz instability

Question 8

Describe Schwarzchild criterion for convective instability?

Answer 8

Positive entropy change in the direction of gravity

Question 9

When are systems gravitationally stable?

Answer 9

When they’re homogenous and static

Question 10

Where is Toomre’s stability criterion applicable?

Answer 10

For gas acreting and differentially rotating disks