Geography Reference
In-Depth Information
and cooling patterns observed in the middle atmosphere are a
result
of the eddies
driving the flow away from a state of radiative balance. This eddy-driven circu-
lation has meridional and vertical wind components that induce substantial local
departures from radiative equilibrium, especially in the winter stratosphere and in
the mesosphere in both winter and summer.
12.2.1
Lagrangian Motion of Air Parcels
Viewed in the conventional Eulerian mean framework (Section 10.2.1), the time-
averaged zonal-mean temperature distribution in the middle atmosphere is deter-
mined by the net balance among net radiative heating or cooling, eddy heat
t
ransp
ort, and adiabatic heating or cooling by the mean meridional circulation
(v, w). That this framework does not provide a useful model for transport in the
meridional plane can be seen easily by considering steady-state adiabatic motion in
the presence of large-scale waves. According to (10.12), in s
uc
h a situation waves
that have a positive poleward heat flux must drive a nonzero w, with upwelling at
high latitudes and downwelling at low latitudes corresponding to the regions of
heat flux convergence and divergence, respectively. However, if the flow is adia-
batic, there can be no motion across the isentr
op
es, and hence in st
ea
dy state there
can be no net vertical transport even though w is nonzero. Thus, w clearly does
not provide an approximation to the vertical motion of air parcels (i.e., the vertical
transport) in such a situation.
But how can vertical transport vanish when the Eulerian mean vertical motion
is finite? The resolution of this “nontransport” paradox can be illustrated by con-
sidering the kinematics of adiabatic flow in the presence of a stationary large-scale
wave superposed on a background westerly flow as shown in Fig. 12.5a. Parcels
moving along the streamlines labeled S
1
,S
2
,S
3
will oscillate about their mean
latitudes, moving equatorward and upward, then poleward and downward follow-
ing the up and down displacements of the isentropic surfaces associated with the
wave. However, over a full wave period there can be no net vertical motion follow-
ing the parcels, as the parcels must remain on the same isentropic surface. Hence
there can be no vertical transport. If, however, an average vertical velocity is com-
puted by taking the mean along a constant latitude circle, then as clearly shown in
Fig. 12.5a, on the latitude cir
cle
φ
3
poleward of the maximum in wave amplitude
the Eulerian mean is upward
[
]
, as regions of upward motion dominate
over regions of downward motion at that latitude. Conversely, on the latitude circle
φ
1
equ
at
orward of the maximum in wave amplitude the Eulerian mean is down-
ward
w (φ
3
) > 0
. The conventional Eulerian mean circulation thus suggests
misleadingly that a trace constituent would be transported upward poleward of the
latitude of maximum wave amplitude and downward equatorward of that latitude.
In reality, air parcels in this idealized example of adiabatic wave motion are not
undergoing net vertical displacements, but are simply oscillating back and forth
[
w (φ
1
) < 0
]
