Geography Reference
In-Depth Information
Fig. 3.8
Relationship between vertical shear of the geostrophic wind and horizontal thickness
gradients. (Note that δp < 0.)
Equations for the rate of change with height of the geostrophic wind compo-
nents are derived most easily using the isobaric coordinate system. In isobaric
coordinates the geostrophic wind (3.4) has components given by
1
f
∂
∂x
1
f
∂
∂y
v
g
=
and
u
g
=−
(3.26)
where the derivatives are evaluated with pressure held constant. Also, with the aid
of the ideal gas law we can write the hydrostatic equation as
∂
∂p
=−
RT
p
α
=−
(3.27)
Differentiating (3.26) with respect to pressure and applying (3.27), we obtain
∂T
∂x
p
∂v
g
∂v
g
∂ ln p
=−
R
f
∂p
≡
(3.28)
p
∂T
∂y
p
∂u
g
∂u
g
∂ ln p
=
R
f
∂p
≡
(3.29)
p
or in vectorial form
∂
V
g
∂ ln p
=−
R
f
k
×
∇
p
T
(3.30)
