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Study Guide (lecture # 13)

Book pages: 130-145

#### Review:

(lecture # 12)

- "Global" definitions of APE

- limited area APE -- Interpretation of:

- efficiency factor

- diabatic processes

#### Today's topics:

- conversion between APE & KE
(mathematical, conceptual, intuitive discussions)

- zonal & eddy energetics (formulas)

#### Jargon:

“closed” domain, “equivalent barotropic”,
non-dimensional form, perturbation form, static state
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

#### Limited area energetics (conclusion):

(Section 4.5.2)
Main point repeatedly seen today:

- **
“warm air rising and/or cold air sinking converts APE into KE”
**

Conversion between APE & KE

- demonstration of link mathematically

- only contributors to average of omega*alpha are by alpha
deviations from horizontal average

- only contributor to (V dot Del Phi) is divergent
advection

- conceptual model for developing & decaying stages

must focus on *relatively* warmer and colder regions

CKA>0 for developing stage (APE -> KE)

CKA<0 for decaying stage

magnitude of CKA during developing stage > than during decay stage

- implies that global average CKA is >0

- expressed in quasi-geostrophic theory as a vertical heat flux, hence:

- "warm air rising and/or cold air sinking converts APE
into KE"

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

#### Eddy versus Zonal Average Energetics:

(Start Section 4.6)

- instead of limited volume, divide APE & KE into [ ] and eddy parts;
calculate zonal mean of each.

- can match terms with what seen before in: (4.16), (4.20), (4.30), and (4.34).

- 4 “reservoirs” of energy: A_{Z}, A_{E},
K_{Z}, K_{E}

- generation (2 terms), destruction (2 terms)

- conversions (4 terms)

- CZ (A_{Z} to K_{Z})
can be approximated using [v] and [u_{g}] which are more
easily measured than [ omega ] and [ alpha ]