ATM 240: Study Guide -- Lecture 18

Study Guide (lecture # 18)

Book pages: 349, plus: 7.3.2: 352-358, 269-281

Review:

(lecture # 17)

Kuo-Eliassen equation (section 6.3)

Today's topics:

eddy life cycle (Chap. 7.3.2)
explanation of: jet entrance, then jet exit regions (Chap. 6.5)

Jargon:

eddy “life cycle”; “sector” averages; jet entrance & jet exit regions; equivalent barotropic vorticity equation

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Eddies and their interaction with the mean flow:

Context:

Lecture #17 showed how meridional ageostrophic circulations maintain thermal wind balance in response to contrary eddy fluxes. This lecture examines the eddies more closely, then combines that information with the previous lecture to tie together the:
- jet stream maxima,
- eddy life cycles,
- tropical convection, and
- ageostrophic circulations.

Frontal cyclone life cycles (part of 7.3.1 (theory), all of 7.3.2 (observations))

emphasize just two basic points:
1. nonlinear evolution enhances upper tropospheric properties of the cyclones
2. energy conversions are: baroclinic growth followed by barotropic decay
upper level enhancement creates:
- double max in vertical for eddy heat fluxes (figs. 7.19 versus 4.31 & 7.22)
- upper level max in eddy momentum fluxes (figs. 7.20 versus 4.12, & 7.23)
energy conversions shown in figs: 7.17 versus 7.24

Eddies and ageostrophic circulations in: jet entrance and jet exit regions (6.5)

items seen to date:
1. conservation of angular momentum
2. momentum and heat fluxes by eddies during their life cycles
3. ageostrophic motions to maintain thermal wind balance (Kuo-Eliassen equation)
4. the long wave pattern
5. preferred regions of tropical convection
cyclone tracks:
- cyclones form near the jet max (small amplitude there)
- proceed along the jet then migrate poleward of the jet
- cyclones have large amplitude downstream and poleward of jet max
jet entrance region:
- since rotational wind >> divergent wind, psi contours should be tight
- tight psi contours between a trough and a ridge
  - trough created by: cold continental air, lee side of mountains
  - ridge created by tropical convection
    - ridge must be displaced from center of convection
    - forced (created) where Rossby wave source, S produces negative vorticity
- ageostrophic wind similar pattern to divergent wind,
  - ageostrophic wind includes tropical divergent wind plus local wind
  - hence, ageostrophic wind is stronger than wind from tropical convection
  - ageostrophic wind created to balance the acceleration (u du/dx)
  - ageostrophic wind looks like extension of Hadley cell (ang. momentum cons.)
jet exit region
- eddy momentum convergence:
  - barotropic decay of eddy
  - despite feeding kinetic energy into mean flow, jet speed decreases. Why?
- Kuo-Eliassen equation finds
  - d/dp ( d (u’v’)/dy ) >0 in upper troposphere here
  - this Kuo-Eliassen forcing creates V_a <0 (i.e. a local “Ferrel” cell)
  - eddy heat fluxes reinforce this “Ferrel” circulation
  - thus, eddy momentum convergence is opposed by local “Ferrel” cell
- kinetic energy equation shows:
  - V_a<0 advects lower geopotential southward
  - “term B” is thus <0, center of mass is also raised (similar to fig. 4.22 )
- contributing factor is time average of jet location that fluctuates wildly due to:
  - passage of large amplitude eddies