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Study Guide (lecture # 11)

Book pages: 111-115, skim: 116

#### Review:

(lecture # 10)

- 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:

potential energy, available potential energy, center of mass, Carnot cycle,
reference state
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#### Available Potential Energy:

(Section 4.3)

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 %