Study Guide (lecture # 14)

Book pages: 146-159

Review:

- conversion between APE & KE (mathematical, conceptual, intuitive discussions)
- zonal & eddy energetics (formulas)

Today's topics:

- conversion between APE & KE (mathematical, conceptual, intuitive discussions)
- zonal & eddy energetics (formulas)

Jargon:

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Eddy versus Zonal Average Energetics:

- energy conversions (cont.)

- "baroclinic" (CA) & "barotropic" (CK)

- key parts are fluxes (CA — heat flux), (CK — momentum flux; as seen in Chap 4.2)
- both CA and CK proportional to a shear in the zonal mean flow
- “eddy grows when tilted against the mean flow shear”
- mature lows migrate to cold side of jet:

- pushes jet equatorward
- CA reverses sign

- CE (A_E -> K_E) discussed in Chap. 4.5.2:

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

- Energy box diagrams

- primary direction of energy flow is G to A to K to D.
- G_Z to A_Z to K_Z is the Hadley cell.
- "express bus route" is A_Z to A_E to K_E (very relevant to frontal cyclones)
- observed values of reservoirs and energy conversions

- domain averages often displayed as "box" diagram (here, we have hemispheric or global averages)
- some terms measured, some are deduced from balance

- energy conversions

- eddy heat fluxes of frontal cyclones: double max in vertical
- eddy momentum fluxes: relate to [u]/R (as noted before, in angular momentum analysis)

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Summary of energy and its flow:

(End of Section 4.6)

Fig. 4.33 shows:

- net excess of energy in tropics (1a), deficit in higher latitudes (2b); net radiation is (1b)
- heat transports in latent & sensible (potential) forms:

- Hadley cell in low latitudes (4) and [v][theta] (not shown)
- midlatitude eddies (4) and (3a)

- transition from Hadley cells (driven in the zonal mean ICZ thunderstorms) to frontal cyclones is complicated; arrows crossing.
- arrows with a "6" require information not yet discussed (e.g. nonlinear eddy evolution)

Energy balance can be viewed as a problem in how energy must be transported (as well as conversion between energy forms)
See table of: Summary of Energy Flow (a web page)
- Energy Flow Table compares: heat and APE with momentum and KE
Some conclusions from the table:

1. net radiation (for APE) and friction (for momentum) create excess (heat and westerlies) in tropics and deficit of (heat and westerlies) in midlatitudes
2. result is meridional fluxes of heat and momentum
3. Key point is that in middle latitudes, eddies are the primary phenomenon to handle all the fluxes.
4. heat fluxes are a net source of eddy energy while momentum fluxes are a net sink of eddy energy.
5. heat flux and kinetic energy flux increase with latitude in subtropics.

(more and more heat must be sent poleward since net radiation >0)
(more and more KE must be sent poleward because CK>0)

6. heat flux a max where net radiation =0; KE flux a max where CK=0. (depending on item 3.)