Geography Reference
In-Depth Information
Fig. 4.9
Schematic view of westerly flow over a topographic barrier: (a) the depth of a fluid column
as a function of x and (b) the trajectory of a parcel in the (x, y) plane.
topographic barrier is shown in Fig. 4.9. In Fig. 4.9a, a vertical cross section of
the flow is shown. We suppose that upstream of the mountain barrier the flow is
a uniform zonal flow so that ζ
0. If the flow is adiabatic, each column of air
of depth h confined between the potential temperature surfaces θ
0
and θ
0
+
=
δθ
remains between those surfaces as it crosses the barrier. For this reason, a potential
temperature surface θ
0
near the ground must approximately follow the ground
contours. A potential temperature surface θ
0
+
δθ several kilometers above the
ground will also be deflected vertically. However, due to pressure forces produced
by interaction of the flow with the topographic barrier, the vertical displacement
at upper levels is spread horizontally; it extends upstream and downstream of the
barrier and has smaller amplitude in the vertical than the displacement near the
ground (see Figs. 4.9 and 4.10).
As a result of the vertical displacement of the upper level isentropes, there
is a vertical stretching of air columns upstream of the topographic barrier. (For
motions of large horizontal scale, the upstream stretching is quite small.) This
stretching causes h to increase, and hence from (4.13) ζ must become positive
in order to conserve potential vorticity. Thus, an air column turns cyclonically
as it approaches the mountain barrier. This cyclonic curvature causes a poleward
drift so that f also increases, which reduces the change in ζ required for potential
vorticity conservation. As the column begins to cross the barrier, its vertical extent
decreases; the relative vorticity must then become negative. Thus, the air column
will acquire anticyclonic vorticity and move southward as shown in the x, y plane
profile in Fig. 4.9b. When the air column has passed over the barrier and returned
to its original depth, it will be south of its original latitude so that f will be smaller
and the relative vorticity must be positive. Thus, the trajectory must have cyclonic
