Study Guide (lecture # 17)

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

Review:

• 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:

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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]

• 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

• 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