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Study Guide (lecture # 10)

Book pages: 96-111

#### Review:

(lecture # 9)

- 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:

tilting with/against shear; wind stress curl; Rayleigh friction;
continental torque; length of day
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

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

(Section 4.2 )

- 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']cos^{2}(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:

(relate to fig. 4.12 & conclude section)

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