Geography Reference
In-Depth Information
planetary vorticity so that - βv
g
> 0. Hence, in region I the advection of relative
vorticity tends to decrease the local vorticity, whereas the advection of planetary
vorticity tends to increase the local vorticity. Similar arguments (but with reversed
signs) apply to region II. Therefore, advection of relative vorticity tends to move
the vorticity pattern and hence the troughs and ridges eastward (downstream).
However, advection of planetary vorticity tends to move the troughs and ridges
westward against the advecting wind field. The latter motion is called
retrograde
motion or
retrogression
.
The net effect of advection on the evolution of the vorticity pattern depends
on which type of vorticity advection dominates. In order to compare the mag-
nitudes of the relative and planetary vorticity advections, we consider an ideal-
ized geopotential distribution on a midlatitude β-plane consisting of the sum of
a zonally averaged part, which depends linearly on y, and a zonally varying part
(representing a synoptic wave disturbance) that has a sinusoidal dependence in
x and y:
(x, y)
=
0
−
f
0
Uy
+
f
0
A sin kx cos ly
(6.20)
Here, y
φ
0
), where a is the radius of the earth and φ
0
is the latitude at
which f
0
is evaluated. The parameters
0
,U, and A depend only on pressure, and
the
wave numbers
k and l are defined as k
=
a(φ
−
2π/L
y
with L
x
and
L
y
the wavelengths in the x andy directions, respectively. The geostrophic wind
components are then given by
=
2π/L
x
and l
=
1
f
0
∂
∂y
=
u
g
=
u
g
=−
U
+
U
+
lA sin kx sin ly
1
f
0
∂
∂x
=
v
g
=+
v
g
=
kA cos kx cos ly
where
u
g
,v
g
is the geostrophic wind due to the synoptic wave disturbance. The
geostrophic vorticity is then simply
k
2
l
2
A sin kx cos ly
f
−
1
0
2
ζ
g
=
∇
=−
+
With the aid of these relations it can be shown that in this simple case the advection
of relative vorticity by the wave component of the geostrophic wind vanishes:
u
g
∂ζ
g
∂x
ν
g
∂ζ
g
∂y
+
=
0
so that the advection of relative vorticity is simply
kU
k
2
l
2
A cos kx cos ly
∂ζ
g
∂x
−
∂ζ
g
∂y
=−
U
∂ζ
g
−
u
g
v
g
∂x
=+
+
