Geography Reference
In-Depth Information
10.3. Compute the me a n zonal wind u at the 200-hPa level at 30˚N under the
assumptions that u
0 at the equator and that the absolute angular momen-
tum is independent of latitude. What is the implication of this result for the
role of eddy motions?
=
10.4. Show by scale analysis that advection by the mean meridional circulation
can be neglected in the zonally averaged equations (10.11) and (10.12) for
quasi-geostrophic motions.
10.5. Show that for quasi-geostrophic eddies the next to last term in square
brackets on the right-hand side in (10.15) is proportional to the vertical
derivative of the eddy meridional relative vorticity flux.
10.6. Starting from equations (10.16)-(10.19), derive the governing equation for
the residual streamfunction (10.21).
10.7. Using the observed data given in Fig. 10.13, compute the time required
for each possible energy transformation or loss to restore or deplete the
observed energy stores. (A watt equals 1 J s 1 .)
10.8. Compute the surface torque per unit horizontal area exerted on the atmo-
sphere by topography for the following distribution of surface pressure and
surface height:
= h sin (kx
p s =
p 0
p sin kx,
h
γ )
10 hPa, h
10 3
where p 0 =
1000 hPa,
p
ˆ
=
=
2.5
×
m,γ
=
π/6 rad, and
k
π/4 radians is the latitude, and a is the radius
of the earth. Express the answer in kg s 2 .
=
1/(a cos φ), where φ
=
10.9. Starting from (10.66) and (10.67) show that the group velocity relative to
the ground for stationary Rossby waves is perpendicular to the wave crests
and has a magnitude given by (10.69).
10.10. Derive the expression of (10.76) for the thermal wind in the dishpan exper-
iments.
10.11. Consider a thermally stratified liquid contained in a rotating annulus of
inner radius 0.8 m, outer radius 1.0 m, and depth 0.1 m. The temperature at
the bottom boundary is held constant at T 0 . The fluid is assumed to satisfy
the equation of state (10.75) with ρ 0 =
10 4 K 1 .
If the temperature increases linearly with height along the outer radial
boundary at a rate of 1 Ccm 1 and is constant with height along the inner
radial boundary, determine the geostrophic velocity at the upper boundary
for a rotation rate of
10 3 kg m 3 and ε
=
2
×
1 rad s 1 . (Assume that the temperature depends
linearly on radius at each level.)
=
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