Geography Reference
In-Depth Information
3.17.
The planet Venus rotates about its axis so slowly that to a reasonable approx-
imation the Coriolis parameter may be set equal to zero. For steady, friction-
less motion parallel to latitude circles the momentum equation (2.20) then
reduces to a type of cyclostrophic balance:
u
2
tanφ
a
1
ρ
∂p
∂y
=−
By transforming this expression to isobaric coordinates, show that the ther-
mal wind equation in this case can be expressed in the form
=
−
R ln (p
0
/p
1
)
(a sin φ cos φ)
∂
T
ω
r
ω
r
(p
0
)
(p
1
)
−
∂y
where R is the gas constant, a is the radius of the planet, and ω
r
≡
u/(a cos φ)
is the relative angular velocity. How must
(the vertically averaged tem-
perature) vary with respect to latitude in order that ω
r
be a function only
of pressure? If the zonal velocity at about 60 km height above the equator
(p
1
T
10
5
Pa)is100ms
−
1
=
2.9
×
and the zonal velocity vanishes at the
10
6
Pa), what is the vertically averaged
temperature difference between the equator and the pole, assuming that ω
r
depends only on pressure? The planetary radius is a
surface of the planet (p
0
=
9.5
×
=
6100 km, and the
187Jkg
−
1
K
−
1
.
=
gas constant is R
3.18.
Suppose that during the passage of a cyclonic storm the radius of curvature
of the isobars is observed to be 800 km at a station where the wind is veering
(turning clockwise) at a rate of 10˚ per hour. What is the radius of curvature
of the trajectory for an air parcel that is passing over the station? (The wind
speed is 20 m s
−
1
.)
3.19.
Show that the divergence of the geostrophic wind in isobaric coordinates on
the spherical earth is given by
cos φ
sin φ
v
g
cot φ
a
1
fa
∂
∂x
∇·
V
g
=−
=−
(Use the spherical coordinate expression for the divergence operator given
in Appendix C.)
3.20.
The following wind data were received from 50 km to the east, north, west,
and south of a station, respectively: 90˚, 10 m s
−
1
; 120˚, 4 m s
−
1
; 90˚,
8ms
−
1
;and60˚,4ms
−
1
. Calculate the approximate horizontal divergence
at the station.
