Geography Reference
In-Depth Information
Fig. 5.6
Schematic surface wind pattern (arrows) associated with high- and low-pressure centers in
the Northern Hemisphere. Isobars are shown by thin lines, and L and H designate high- and
low-pressure centers, respectively. After Stull (1988).
=
0. Assuming again that v
g
=
where we have assumed that w(0)
0 so that u
g
is
independent of x, we find after substituting from (5.31) into (5.36) and comparing
with (5.35) that the mass transport at the top of the Ekman layer is given by
∂M
∂y
ρ
0
w(De)
=−
(5.37)
Thus, the mass flux out of the boundary layer is equal to the convergence of the
cross isobar mass transport in the layer. Noting that
ζ
g
is just the
geostrophic vorticity in this case, we find after integrating (5.35) and substituting
into (5.37) that
5
−
∂u
g
/∂y
=
ζ
g
1
2γ
ζ
g
f
|
f
|
1/2
K
m
2f
w(De)
=
=
(5.38)
where we have neglected the variation of density with height in the boundary layer
and have assumed that 1
e
-
π
1. Hence, we obtain the important result that the
vertical velocity at the top of the boundary layer is proportional to the geostrophic
vorticity. In this way the effect of boundary layer fluxes is communicated directly
to the free atmosphere through a forced
secondary circulation
that usually dom-
inates over turbulent mixing. This process is often referred to as
boundary layer
pumping
. It only occurs in rotating fluids and is one of the fundamental distinctions
between rotating and nonrotating flow. For a typical synoptic-scale system with
ζ
g
+
≈
10
−
5
s
−
1
, f
10
−
4
s
−
1
, and De
1 km, the vertical velocity given by
(5.38) is of the order of a few millimeters per second.
An analogous boundary layer pumping is responsible for the decay of the circu-
lation created when a cup of tea is stirred. Away from the bottom and sides of the
∼
∼
∼
5
The ratio of the Coriolis parameter to its absolute value is included so that the formula will be
valid in both hemispheres.
