Geography Reference
In-Depth Information
Equation (10.43) expresses the angular momentum budget for a zonal ring of air
of unit meridional width, extending from the ground to the top of the atmosphere.
In the long-term mean the three terms on the right, representing the convergence of
the meridional flux of angular momentum, the torque due to small scale turbulent
fluxes at the surface, and the surface pressure torque, must balance. In the sigma
c
oordinate s
ystem the surface pressure torque takes the particularly simple form
−
p
s
∂h
∂x . Thus, the pressure torque acts to transfer angular momentum from
the atmosphere to the ground, provided that the surface pressure and the slope
of the ground (∂h/∂x) are correlated positively. Observations indicate that this is
generally the case in middle latitudes because there is a slight tendency for the
surface pressure to be higher on the western sides of mountains than on the east-
ern sides (see Fig. 4.9). In midlatitudes of the Northern Hemisphere the surface
pressure torque provides nearly one-half of the total atmosphere-surface momen-
tum exchange; but in the tropics and the Southern Hemisphere the exchange is
dominated by turbulent eddy stresses.
The role of eddy motions in providing the meridional angular momentum trans-
port necessary to balance the surface angular momentum sinks can be elucidated
best if we divide the flow into zonal-mean and eddy components by letting
M
=
a cos φ
u
a cos φ
M
=
M
+
+
u
+
(p
s
v)
p
s
v
=
(p
s
v)
+
where primes indicate deviations from the zonal mean. Thus, the meridional flux
becomes
a cos φp
s
v
u
(p
s
v)
a cos φ
(p
s
Mv)
=
+¯
up
s
v
+
(10.44)
The three meridional flux terms on the right in this expression are called the merid-
ional -momentum flux, the meridional drift, and the meridional eddy momentum
flux, respectively.
The drift term is important in the tropics, but in midlatitudes it is small compared
to the eddy flux and can be neglected in an approximate treatment. Furthermore,
we can show that the meridional -momentum flux does not contribute to the
vertically integrated flux. Averaging the continuity equation (10.34) zonally and
integrating vertically, we obtain
1
∂p
s
∂t
=−
(
cos φ
)
−
1
∂
∂y
p
s
v cos φdσ
(10.45)
0
Thus, for time-averaged flow [where the left-hand side of (10.45) vanishes] there
is no net mass flow across latitude circles. The vertically integrated meridional
