Geography Reference
In-Depth Information
6.8.
For the geopotential field of Problem 6.7, use the omega equation (6.36)
to find an expression for ω for the conditions in which χ
=
0.
Hint
: Let
ω
W
0
cos kxsin(πp/p
0
) where W
0
is a constant to be determined. Sketch
a cross section in the x, p plane indicating trough and ridge lines, vorticity
maxima and minima, vertical motion and divergence patterns, and locations
of maximum cold and warm temperature advection.
=
6.9.
Given the following expression for the geopotential field,
f
0
ct)
k
−
1
V cos (πp/p
0
) sin k (x
(x, y, p)
=
0
(p)
+
−
Uy
+
−
where U , V , and c are constant speeds, use the quasi-geostrophic vorticity
equation (6.19) to obtain an estimate of ω. Assume that df/dy
=
β is a
p
0
.
6.10.
For the conditions given in Problem 6.9, use the adiabatic thermodynamic
energy equation to obtain an alternative estimate for ω. Determine the value
of c for which this estimate of ω agrees with that found in Problem 6.9.
constant (
not zero
) and that ω vanishes for p
=
6.11.
For the conditions given in Problem 6.9, use the omega equation (6.36) to
obtain an expression for ω. Verify that this result agrees with the results
of Problems 6.9 and 6.10. Sketch the phase relationship between and
ω at 250 and 750 hPa. What is the amplitude of ω ifβ
10
−
11
m
−
1
s
−
1
,
=
×
2
25 m s
−
1
,V
8ms
−
1
,k
2π/(10
4
km), f
0
10
−
4
s
−
1
,σ
=
=
=
=
=
U
10
−
6
Pa
−
2
m
2
s
−
2
, and p
0
=
2
×
1000 hPa?
6.12.
Compute the
Q
vector distributions corresponding to the geopotential fields
given in Problems 6.4 and 6.7.
6.13.
Show that the isallobaric wind may be expressed in the form
f
−
2
0
V
isall
=−
∇
χ
where χ
=
∂/∂t .
MATLAB EXERCISES
M6.1.
Suppose that the 500-hPa geopotential field has the following structure
(expressed in m
2
s
−
1
):
10
4
Vf
0
k
−
1
sin [k (x
=
5.5
×
−
U
0
f
0
y
+
−
ct)] cos ly
10
−
4
s
−
1
, V
25ms
−
1
, c
25ms
−
1
,
where U
0
=
30 m/s, f
0
=
1.0
×
=
=
2π
L
x
, and l
2π
L
y
where L
x
10
6
k
=
=
=
6
×
m and L
y
=