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Study Guide (lecture # 17)

Book pages: 254-264; skim: 249-254

#### Review:

(lecture # 16)
- zonal variations of: P, moisture, momentum flux, heat flux, storm tracks,
Asian monsoon
- Sections: 5.4, 5.5, 5.6, 5.7, 5.9 (skip 5.8)

#### Today's topics:

- Kuo-Eliassen equation (section 6.3)

#### Jargon:

thermal wind balance, cannonical form
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#### Kuo-Eliassen Equation (Chap. 6.3):

Context:

- Fig. 3.17 uses [Psi] to show [v] and [omega]
- Fig. 5.7 shows relation between du/dx and ageostrophic v
- Chap. 6.2.3.2 deduces [u] from specified [v]
- Carnot cycle specifies a [Psi] motion to obtain rate of energy conversion in Hadley cell
- Kuo-Eliassen equation specifies [u], [theta], eddy fluxes and diabatic rates to obtain
[Psi]

Derivation: (section 6.3.1)
- Use thermal wind balance to combine zonal momentum and adiabatic equations.
- Zonal averages taken,
- Stationary solutions sought: combining the 2 equations eliminates time derivatives.
- Final equation
- is a linear, nonhomogeneous, 2-D, P.D.E. operating on
- has 4 forcings: eddy heat and momentum fluxes, diabatic heating, friction

Interpretation: (section 6.3.2)
- Determination of canonical form:
- it is elliptic
- approximate operator with a “minus” sign (for qualitative interpretation)

- Sample solution: rising where heating is a max, sinking where it is a (negative max) minimum
- Analysis of circulation induced by each forcing
- since operator is linear, has separate contributions from each forcing
- eddy fluxes:
- neglect vertical fluxes in favor of meridional fluxes
- both heat and momentum fluxes create Ferrel and Hadley cells.
- heat and momentum fluxes drive atmosphere away from thermal wind balance
- [v] and [omega] circulation brings atmosphere back into thermal wind balance

- the climate is maintained by a balance between eddy fluxes and meridional circulations
- diabatic heating:
- creates Hadley cell (mainly due latent heating from ICZ precipitation)
- creates Ferrel (mainly due to latent heating from eddy-induced precipitation)
- might create polar cell (from high latitude radiational cooling and eddy precipitation)

- friction: small but somewhat unclear forcing, possible Hadley and Ferrel cells