3. Convection

Question 1

What is convection?

Answer 1

Transport of heat/concentrations due to bulk motion in the fluid induced by buoyancy arising from heat/concentration differences.

Question 2

What is the Rayleigh number?

Answer 2

Ra=densitygaH^3theta/mew*k

If Ra>1708 (critical value of Rayleigh number) convection motion will start to occur.

Question 3

What are the initial flux equations?

Answer 3

Q=Aw
M=Aw^2
F=g’Aw

Question 4

What is a pure plume?

Answer 4

A continuous, buoyancy driven flow.

Mo=0, Qo=0, Fo>0

Question 5

What is a pure jet?

Answer 5

A continuous, momentum driven flow.

Mo>0, Qo=0, Fo=0

Question 6

What happens further away from the plume source?

Answer 6

As the plume propagates, turbulence causes it to mix and entrain ambient fluid.

Question 7

What is the entertainment assumption and why is it necessary?

Answer 7

horizontal velocity ue is proportional to the plume vertical velocity.
Assumption necessary to close plume eqns in Q M and F
Reasonable if the level of turbulence in the plume is both generated by vertical velocities and the key driving in entertainment (generation of eddies at edge)

Question 8

What are the assumptions of the plume derivation?

Answer 8

1. Continuous buoyancy force
2. Ambient at rest
3. No input or sink of buoyancy in the plume
4. Background ambient is unstratified
5. Entrainment assumption
6. Top hat model (Plume quantities well mixed across radius & zero outside)

Question 9

What is the spreading angle of a plume? Of a jet?

Answer 9

plume = 7 degrees
jet = 11 degrees

Question 10

Describe the formation of a volcanic flume

Answer 10

1. Gas thrust: Hot rocks & volcanic gas ejected under pressure -driven by momentum
2. Convective Region: rocks fall out of system. Heated gases are buoyant compared to ambient - buoyancy
3. Umbrella Cloud: plume spreads out at neutrally buoyant level.