Geoscience Reference
In-Depth Information
Figure 10.5
A schematic illustration
of the density field and flow driven by
the JEBAR process along the shelf
slope. The figure is drawn for the
northern hemisphere. Adapted from
Hill,
1998
, courtesy John Wiley &
Sons.
V(x,y)
r
+
r
r
-
r
+
r
r
-
y
U
x
h(x)
U
depth h(x) is a function of x only. The steady state, vertically integrated equations of
motion for frictionless, linear flow can then be written:
g
]
]
g
]
]
g
0
]
y
h
2
fV
¼
x
h
;
fU
¼
y
h
ð
10
:
8
Þ
2
]
where U and V are the vertically integrated transports in x and y. Again, we want to know
how this flow will vary horizontally while maintaining flow continuity, so we differentiate
these equations with respect to y and x respectively and combine with the continuity equation
U
]
V
]
]
x
þ
]
y
¼
0
ð
10
:
9
Þ
to give the meridional surface slope as:
]
]
0
]
h
y
¼
y
:
ð
10
:
10
Þ
]
For the shelf (h
¼
h
s
), and the deep ocean (h
¼
H), the surface slopes will be:
h
s
¼
H
¼
]
]
0
]
]
]
0
]
h
s
H
y
;
y
:
ð
10
:
11
Þ
y
y
]
]
Since H
h
s
the downward slope with latitude will be greater over the deep ocean
and, in consequence, the difference between sea surface height over the shelf and that
over the ocean will increase with latitude, as is illustrated schematically in
Fig. 10.5
.
This difference will result in a geostrophic current parallel to the isobaths. At the
same time, the dynamical balance in the y direction implies a geostrophic transport in
deep water towards the slope of:
gH
2
2
0
f
]
U
¼
y
:
ð
10
:
12
Þ
]
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