Geography Reference
In-Depth Information
forth between regimes in a chaotic fashion. Whether the high-index and low-index
states actually correspond to distinct quasi-stable atmospheric climate regimes
is a matter of controversy. The general notion of vacillation between two quasi-
stable flow regimes can, however, be demonstrated quite convincingly in laboratory
experiments. Such experiments are described briefly in Section 10.7.
The concept of climate regimes can also be demonstrated in a highly simpli-
fied model of the atmosphere developed by Charney and DeVore (1979). They
examined the equilibrium mean states that can result when a damped topographic
Rossby wave interacts with the zonal-mean flow. Their model is an extension
of the topographic Rossby wave analysis given in Section 7.7.2. In this model
the wave disturbance is governed by (7.99), which is the linearized form of the
barotropic vorticity equation (7.94) with weak damping added. The zonal-mean
flow is governed by the barotropic momentum equation
∂u
∂t
=−
D (u)
−
κ (u
−
U
e
)
(10.71)
where the first term on the right designates forcing by interaction between the waves
and the mean flow, and the second term represents a linear relaxation toward an
externally determined basic state flow, U
e
.
The zonal mean equation (10.71) can be obtained from (7.94) by dividing the
flow into zonal mean and eddy parts and taking the zonal average to get
v
g
ζ
g
v
g
h
T
∂
∂t
∂u
∂y
∂
∂y
f
0
H
∂
∂y
−
=−
−
which after integrating in y and adding the external forcing term yields (10.71) with
v
g
ζ
g
−
f
0
H
v
g
h
T
D (u)
=−
(10.72)
As shown in Problem 10.5, the eddy vorticity flux [the first term on the right in
(10.72)] is proportional to the divergence of the eddy momentum flux. The second
term, which is sometimes referred to as the
form drag
, is the equivalent in the
barotropic model of the surface pressure torque term in the angular momentum
balance equation (10.43).
If h
T
and the eddy geostrophic streamfunction are assumed to consist of single
harmonic wave components in x and y, as given by (7.96) and (7.97), respec-
tively, the vorticity flux vanishes, and with the aid of (7.100) the form drag can be
expressed as
rK
2
f
0
2uH
2
f
0
H
v
g
h
T
h
0
cos
2
ly
D (u)
=−
=
K
2
ε
2
(10.73)
K
s
2
−
+
