The shelf edge system - Introduction to the Physical and Biological Oceanography of Shelf Seas - page 319

Fig. 10.10c . In this case, the biogeochemistry of the descending plume of water
provided tracers that confirmed the shelf origin; for instance Fig. 10.10d shows that
the plume had a distinctive chlorophyll signature.
We can apply the dynamical balance (10.19) to these observations at the Malin
shelf edge. Taking parameter values of: h 10 4 s 1 ; r 10 4

¼ 50 m; f ¼ 1.19 ¼ 7.5

ms 1 ; g 0 ¼ 10 4 ms 2 ; d 4.5 ; we find: y 7 ; V g ' 0.07 m s 1 . This indicates an

¼ '

7cms 1 inclined at a small angle of 7 to the isobaths,
which implies a downslope speed of 0.8 cm s 1 and a corresponding downslope
transport of

almost geostrophic flow of ∼

0.4 m 2 s 1 . In this case, therefore, cascading appears to induce a
contribution to cross-slope transport which is of the same order, and in the same
direction, as that due to the Ekman drainage forced by the slope current. Cascading
due to differential cooling, however, operates only for short periods (a few days) so
its average transport will not generally compete with the more persistent influence of
Ekman drainage.
As the cascading water descends, it tends to mix with the overlying slope water so
that its excess density

∼

r decreases and the downslope flow will diminish as the
cascade reaches an equilibrium level (

D

∼

500 metres in the Malin shelf example) where
its density matches that of the ambient water. More elaborate models of the cascad-
ing process allow for the entrainment of ambient water into the descending plume
and, in principle, can predict the equilibrium depth, although uncertainties remain
about the friction and entrainment parameters in such models.
Cascading is not limited to differential cooling at the shelf edge. An alternative
forcing mechanism is the production of high-salinity water on the shelf in arid
regions which are subject to high evaporation as we saw in Section 2.3.4 for
Spencer Gulf, South Australia. Cascading in the Gulf, down the slope to

250 metres
depth, commences at the end of the summer season and, over a period of about
3 months, drains the high-salinity water accumulated in the Gulf during the previous
summer (Lennon et al., 1987 ). Cascades are potentially an important source of shelf
water to the deeper ocean, transporting heat, salt and carbon. A global inventory of
61 confirmed cases of cascading has led to a tentative estimate of a cascade trans-
porting between 0.05 and 0.08 Sv per 100 km of shelf edge, or 0.5-0.8 m 3 s 1 per
metre length of slope (Ivanov et al., 2004 ). One final point to consider is that, in lower
latitudes, the advent of large-scale desalination plants to alleviate water shortages in
arid regions will lead to substantial enhancement of salinity. Such plants could
therefore generate local cascading effects which may significantly modify the local
shelf environment.

∼

10.3.4 Meandering and eddies

If the flow along the slope encounters abrupt changes in the direction of the isobars,
forcing the current to meander and go round 'tight corners', the non-linear terms in
the dynamical equations may become significant and the flow will not be geostrophic.
In setting up the geostrophic balance, we assumed that the non-linear terms (v ] u
]

y etc.)

could be neglected so that D Dt ¼ ] u

t . This linearising assumption is not valid when the

]