Geography Reference
In-Depth Information
8
4
0
-4
-8
80
°
S60
0
20
60
40
20
40
80
°
N
Fig. 10.12
Latitudinal profile of the annual mean eastward torque (surface friction plus mountain
torque) exerted on the atmosphere in units of 10
18
m
2
kg s
−
2
. (Adapted from Oort and
Peixoto, 1983.)
10.4
THE LORENZ ENERGY CYCLE
The previous section discussed the interaction between zonally averaged flow and
longitudinally varying eddy motions in terms of the angular momentum balance.
It is also useful to examine the exchange of energy between the eddies and the
mean flow. As in Section 10.2, we limit the analysis to quasi-geostrophic flow on
a midlatitude β plane. Eulerian mean equations in log-pressure coordinates can
then be written as
∂
u
v
∂y
∂u
∂t
−
f
0
v
=−
+
X
(10.47)
∂
∂y
f
0
u
=−
(10.48)
∂
∂z
v
∂
∂z
∂
∂t
κ
H
J
∂
∂y
wN
2
+
=
−
(10.49)
∂v
∂y
∂
(
ρ
0
w
)
∂z
ρ
−
1
0
0 (10.50)
Here we have used the hydrostatic approximation in (10.3) to express the temper-
ature in (10.49) in terms of the differential geopotential thickness, and we have
again neglected vertical eddy fluxes and advection by the mean meridional circu-
la
tion in (10.47) and (10.49). We have, however, included a turbulent drag force,
X, in (10.47), as dissipation by unresolved turbulent eddies is an essential element
in the energy balance.
+
=
