Summary of momentum cycle in atmosphere


Angular momentum follows a cycle in the atmosphere. Except as noted, much of what follows may be deduced from information plotted in figure 4.12 (p. 110).
  1. Surface easterlies impart westerly momentum into the lower troposphere in the tropics.
  2. The rising motion in the Hadley cell (convection) brings that momentum up to the upper troposphere.
  3. The Hadley cells (and summertime mid-ocean troughs) carry that momentum across the subtropics. Angular momentum conservation builds [u] at upper levels. (Chap. 6.2.3.2). We may see the link between the Hadley cells and the ZONAL AVERAGE subtropical jet. "Fig. 9.13" from Newton shows monthly values of zonal mean zonal wind (contours). Shaded areas denote [u]>30 m/s. The dashed lines mark the jet axes. The arrows with dots show the upper level mass flux by the Hadley cell (in most cases, the winter one). Notice how the subtropical jet speeds correlate nicely with the mass flux. The stronger the cell, the stronger the jet.
  4. The vertical shear of the [u] subtropical jet favors eddy growth. (Chap. 4.6; term "CA")
  5. Eddies have [u'v'] >0 that continues the flux of momentum poleward. From the [KZ] eqn (4.12) and fig 9.8 from Newton (1972), these fluxes maintain the westerlies against frictional loss.
  6. [u'v'] flux reaches a maximum near 30o latitude. Flux convergence on the poleward side stimulates the formation of a (Ferrel cell) [v]<0 at upper levels. The meridional flux of planetary angular momentum by the Ferrel cell opposes the flux by the eddies. (Eddy fluxes cause westerly acceleration, but [v]<0 create easterly acceleration.) Hence, the location of maximum [u] is equatorward of the maximum [u'v'] convergence. Divergence of eddy momentum flux on the equatorward side of the [u'v'] maximum reinforces the Hadley circulation in the subtropics.
  7. Correlations between eddy vertical and eddy zonal winds mixes the westerly momentum back down into the lower troposphere.
  8. Surface friction removes the westerly momentum, either directly into the ground or injects it into the oceans which pass it along into the ground.

 
Schematic Momentum Flow
            The illustration below may be associated with "fig. 13" from Oort & Peixoto (1983). The O&P (1983) chart is a zonal cross section, as is the simplified chart below. The streamlines in O&P's figure nicely show the westerly angular momentum source in the subtropics, transport poleward, followed by the sink in the middle latitudes. Their chart shows a streamfunction calculated from the zonal momentum equation without the meridional transport of planetary angular momentum by [v]. (i.e. without the Omega[v] term). The result is to keep the [u][v], [u][omega], the eddy fluxes, and the friction.
            The eight "steps" in the momentum cycle listed above are identified by numbers on the chart below. Crudely drawn arrows show the same direction of momentum transport in the chart below.
            Note: this table may not display properly in the microsoft internet explorer browser. I plan to produce an image file someday...

The 8 steps:
|   |
|   < -- 5 --    <- 5 -   < -- 3 --       |
|   -- 6 -- >     4       /\   |
|           |            2   |
|           7             |   |
|           \/             1-->       |
|____________   __\/8__   _______________   __/\___   _________   |
NP   60    30   <-- latitude         EQ