Study Guide (lecture # 10)

Book pages: 96-111

Review:

- momentum balance (viewed as a KE tendency problem) (Start Chapter 4.2)

Today's topics:

- momentum balance (viewed as a KE tendency problem) (Finish Chapter 4.2)
- summary of momentum cycle

Jargon:

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momentum maintenance (cast as a problem in KE change) concluded:

- 1. eddy shape and energy conversions

eddy titled against the shear grows; with the shear feeds eddy energy to mean flow

- 2. affect of atmospheric torques upon ocean circulation;

- connection to atmospheric wind stress (curl)
- western boundary currents
- oceanic torque upon solid earth

- 3. Seasonal change & LOD

M_air greater in DJF than JJA
partial compensation by mass redistribution by atmosphere
link M_air to M_{solid earth} by: stronger westerlies associated with a stronger Hadley cell
stronger total zonal winds imply slower rotation of solid earth

4. what [u'v'] implies about [v] (relate to Gill's eqn. 13.10.4 (p. 583) but use P coordinate)

[M] has monotone gradient, <0 in NH
[u'v'] largest in upper troposphere (fig. 4.11)
[v]=0 between Hadley & Ferrel cells, which implies:

[u'v'] creates Ferrel cell (upper level) but also upper level of Hadley cell

[v] changes sign where [u'v']cos²(phi) is a maximum

friction (fig. 4.6) consistent with lower level Ferrel and Hadley circulations

[omega] transports angular momentum up in tropics, [u' omega'] down in midlatitudes

Summary of momentum cycle:

1. Friction inputs westerly momentum in tropics
2. Hadley circulations (convection) transport momentum to upper troposphere
3. Hadley cells (partly driven by eddies) transport [M] poleward in subtropics
4. Stronger the Hadley cell, the stronger [u] of subtropical jet (fig. 9.13 in Newton, 1972)
5. [u] max helps eddies form that handle [M] transport in subtropics & midlatitudes
6. Eddies have vertical mixing of westerly momentum brings some down to surface
7. Friction removes westerly momentum in middle latitudes