Geography Reference
In-Depth Information
latitudes by regions of strong meridional gradients of long-lived tracers and of
PV. The existence of such gradients is evidence that there is only weak mix-
ing into and out of the tropics and into and out of the polar winter vortex. Thus
these locations are sometimes referred to as “transport barriers.” The strong PV
gradients, strong winds, and strong wind shears that occur along the transport bar-
riers at the subtropical and polar edges of the surf zone all act to suppress wave-
breaking, and hence to minimize mixing and sustain the strong gradients at those
locations.
PROBLEMS
12.1.
Suppose that temperature increases linearly with height in the layer between
20 and 50 km at a rate of 2 K km
−
1
. If the temperature is 200 K at 20 km,
find the value of the scale height H for which the log-pressure height z
coincides with actual height at 50 km. (Assume that z coincides with the
actual height at 20 km and let g
9.81ms
−
2
=
be a constant.)
12.2.
Find the Rossby critical velocities for zonal wave numbers 1, 2, and 3 (i.e.,
for 1, 2, and 3 wavelengths around a latitude circle). Let the motion be
referred to a β plane centered at 45
◦
N, scale height H
=
7 km, buoyancy
10
−
2
s
−
1
, and infinite meridional scale (l
frequency N
=
2
×
=
0).
12.3.
Suppose that a stationary linear Rossby wave is forced by flow over sinu-
soidal topography with height h(x)
h
0
cos (kx), where h
0
is a constant
and k is the zonal wave number. Show that the lower boundary condition
on the streamfunction ψ can be expressed in this case as
=
hN
2
/f
0
(∂ψ/∂z)
=−
Using this boundary condition and an appropriate upper boundary condi-
tion, solve for ψ (x, z) in the case
(1/2H ) using the equations of
Section 12.3.1. How does the position of the trough relative to the mountain
ridge depend on the sign of m
2
|
m
|
for the limit
|
m
|
(1/2H).
12.4.
Consider a very simple model of a steady-state mean meridional circu-
lation for zonally symmetric flow in a midlatitude channel bounded by
walls at y
0,π/m. We assume that the zonal mean
zonal flow u is in thermal wind balance and that the eddy momentum and
heat fluxes vanish. For simplicity, we let ρ
0
=
0,π/land z
=
1 (Boussinesq approxi-
mation) and let t
he
zonal f
or
ce due to small-scale motions be represented
by a linear drag: X
=
=−
γ u. We assume that the diabatic heating has the
form J/c
p
=
(H/R) J
0
cos ly sin mz, and we let N and f be constants.
