Geography Reference
In-Depth Information
meters per kilometer horizontal distance) assuming a steady pressure field,
geostrophic winds, and f
10
−
4
s
−
1
?
=
3.2.
The actual wind is directed 30
◦
to the right of the geostrophic wind. If the
geostrophic wind is 20 m s
−
1
, what is the rate of change of wind speed? Let
f
10
−
4
s
−
1
.
=
3.3.
A tornado rotates with constant angular velocity ω. Show that the surface
pressure at the center of the tornado is given by
p
0
exp
ω
2
r
0
2RT
−
p
=
where p
0
is the surface pressure at a distance r
0
from the center and T is the
temperature (assumed constant). If the temperature is 288 K and pressure
and wind speed at 100 m from the center are 1000 hPa and 100 m s
−
1
,
respectively, what is the central pressure?
3.4.
Calculate the geostrophic wind speed (m s
-
1
) on an isobaric surface for a
geopotential height gradient of 100 m per 1000 km and compare with all
possible gradient wind speeds for the same geopotential height gradient and
a radius of curvature of
10
−
4
s
−
1.
±
500 km. Let f
=
3.5.
Determine the maximum possible ratio of the normal anticyclonic gradient
wind speed to the geostrophic wind speed for the same pressure gradient.
3.6.
Show that the geostrophic balance in isothermal coordinates may be written
f
V
g
=
k
×
∇
T
(RT ln p
+
)
3.7.
Determine the radii of curvature for the trajectories of air parcels located
500 km to the east, north, south, and west of the center of a circular low-
pressure system, respectively. The system is moving eastward at 15 m s
−
1
.
Assume geostrophic flow with a uniform tangential wind speed of 15 m s
−
1
.
3.8.
Determine the normal gradient wind speeds for the four air parcels of Prob-
lem 3.7 using the radii of curvature computed in Problem 3.7 Compare
these speeds with the geostrophic speed. (Let f
10
-
4
s
-
1
.) Use the gra-
dient wind speeds calculated here to recompute the radii of curvature for
the four air parcels referred to in Problem 3.7. Use these new estimates of
the radii of curvature to recompute the gradient wind speeds for the four air
parcels. What fractional error is made in the radii of curvature by using the
geostrophic wind approximation in this case? [Note that further iterations
could be carried out but would converge rapidly.]
=
