Geoscience Reference
In-Depth Information
F
v
=
rV
g
/h
(
f cos
d
)
V
g
θ
g
I
sin
d
V
g
d
Figure 10.8
Forces acting in the plane of the slope during a steady flow of a layer of
thickness h down a uniform slope at a speed V
g
. The gravitational force due to the excess
density of the cascading flow acts down the slope and is balanced by the Coriolis force (f cos d)
V
g
acting to the right of the flow (northern hemisphere) and a drag force F
v
induced by
friction at the top and bottom boundaries of the flow.
where V
g
is the speed of the flow, which is assumed to be vertically uniform in the
cascading layer. In deriving Equations (
10.17
) and (
10.18
) we have neglected a small
contribution from the horizontal component of the Earth's rotation. The frictional
term F
v
represents the combined frictional stresses at the top and bottom of the
cascading layer. If we assume that F
v
can be represented by a linear drag law of the
form F
v
¼
rrV
g
, then the flow direction and speed are given by:
g
0
h sin
g
0
h
r
fh cos
r
fh
;
f
2
h
2
cos
2
f
2
h
2
tan
¼
V
g
¼
p
p
ð
10
:
19
Þ
þ
r
2
þ
r
2
15
. Bowden (Bowden,
1960
)
first applied this relation to show that the flow of dense water along the sides of the
Iceland-Faroes ridge was descending at an angle of 5-10
relative to the isobaths.
The results in Equation (
10.19
) apply to flow on a slope which is uniform in the along-
shelf direction. Where the along-slope topography is punctuated by canyons running
down the slope, the density current will tend to concentrate in the canyons whose walls
can support the component of the pressure gradient normal to the flow which is needed
to balance the Coriolis force in a purely downslope flow. This is illustrated in
Fig. 10.9
,
which is based on the results of a high-resolution 3-dimensional numerical model of
cascading down an idealised canyon (Chapman and Gawarkiewicz,
1995
). A section
down the central axis of the canyon, in
Fig 10.9a
, shows the higher density water moving
down the slope. Looking in the direction of the downslope flow at a section across the
canyon (
Fig. 10.9b
), the effect of the Coriolis force is clear as the core of the flow is
displaced towards the right-hand wall of the canyon (northern hemisphere).
We might expect cascading events forced by differential cooling to occur infre-
quently, probably not more than once per year at the end of the winter cooling
period. They will, moreover, be short-lived features since the cascade flow will rapidly
eliminate the density instability. Such infrequent events of short duration at the shelf
edge are difficult to observe.
Fig. 10.10
shows one of the few recorded examples - an
event which occurred at the Malin shelf edge west of Ireland near the end of winter
where the final steps are valid approximations when d
<
Search WWH ::
Custom Search