Geography Reference
In-Depth Information
Equations (12.1), (12.2), (12.3), and (12.4) then yield the following:
f
0
v
∗
=−
−
γ u
N
2
HR
−
1
w
∗
=+
+
J/c
p
∂χ
∗
∂z
;
∂χ
∗
∂y
v
∗
=−
w
∗
=
RH
−
1
∂T/∂y
0
Assuming that there i
s n
o
flo
w thr
ou
gh the walls, solve for the residual
circulation defined by χ
∗
, v
∗
, and w
∗
.
f
0
∂u/∂z
+
=
12.5.
For the situation of Pr
o
blem
1
2.4, solve for the steady-state zonal wind
and temperature fields u and T .
12.6.
Find the geopotential and vertical velocity fluctuations for a Kelvin wave
of zonal wave number 1, phase speed 40 m s
−
1
, and zonal velocity pertur-
bation amplitude5ms
−
1
. Let N
2
10
−
4
s
−
2
.
12.7.
For the
situa
tion of Problem 12.6 compute the vertical momentum flux
M
=
4
×
ρ
0
u
w
. Show that M is constant with height.
12.8.
Determine the form for the vertical velocity perturbation for the Rossby-
gravity wave corresponding to the u
, v
, and
≡
perturbations given
in (12.44).
12.9.
For a Rossby-gravity wave of zonal wave number 4 and phase speed
−
20 m
s
−
1
, d
etermine the latitude at which the vertical momentum flux
M
ρ
0
u
w
is a maximum.
12.10.
Suppose that the mean zonal wind shear in the descending westerlies of the
equatorial QBO can be represented analytically on the equatorial β plane
in the form ∂u/∂z
≡
exp
−
y
2
/L
2
where L
1200 km. Determine
the approximate meridional dependence of the corresponding temperature
anomaly for
=
=
L.
12.11.
Estimate the TEM residual vertical velocity in the westerly shear zone of
the equatorial QBO assuming that radiative cooling can be approximated
by Newtonian cooling with a 20-day relaxation time, that the vertical shear
is 20 m s
−
1
per 5 km, and that the meridional half-width is 12
◦
latitude.
|
y
|
MATLAB EXERCISES
M12.1.
The MATLAB script
topo Rossby wave.m
plots solutions for various
fields for a stationary linear Rossby wave forced by flow over an iso-
lated ridge. A β-plane channel model is used following the discussion in
