Study Guide (lecture # 11)

Book pages: 111-115, skim: 116

Review:

- momentum balance (viewed as a KE tendency problem)finish Chap. 4.2
- summary of momentum cycle

Today's topics:

- potential energy considerations
- introduction to APE, conceptual models

Jargon:

+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

Available Potential Energy:

Previously: given KE we explained the angular momentum cycle.

- Now we want to understand where the motions come from

The basic concept of APE:

- What is PE? (gravitational and internal parts)
- Why is only part of it "available"?

3 simple models illustrating APE:

1. pendulum model

- if total energy conserved, then minimum KE is max PE & vice-versa
- only the difference between max and min PE is actually “available” for KE
- reference state & thus minimum APE arbitrary

2. Two-fluid model (fig. 4.13)

- fluid "equivalent" of the pendulum model
- density difference between the fluids proportional to APE

Application to the atmosphere:

- tropics vs polar regions density differences proportional to APE
- reference state must be motionless

- geostrophic balance links APE and KE
- APE minimum, with geostrophic KE=0 for “flat” P and surfaces

3. Carnot cycle model

- review
- applicable to the Hadley cell
- circuit around Hadley cell encloses area on a skew-T chart
- estimating total energy input (absorbed solar radiation)
- estimating total energy released (work done to create air motions)
- efficiency of the atmospheric “heat engine” is a few %