The shelf edge system - Introduction to the Physical and Biological Oceanography of Shelf Seas - page 316

transport in the bottom boundary layer, with a compensating offshore flow in the
upper part of the water column, is thought to contribute significantly to the supply of
nutrients to the shelf (Condie, 1995 ). In both cases the transport in the bottom
Ekman layer is the result of bed friction, and so the bottom Ekman layer will be
turbulent. This turbulence will result in a mixed near-bed layer, the observation of
which is a useful indicator of near-bed cross-slope flow.
Transport in the surface and bottom Ekman layers may reinforce or oppose each
other, but their average effect can be a major contribution to cross-slope exchange.
For the European shelf region between 54 N to 57N, the net flux, forced by surface
and bottom boundary layer motions for the period 1960-2004, has been estimated
from a full-physics model as a net downwelling transport of 1.75 m 2 s 1

(Holt and

Proctor, 2008 ). The corresponding horizontal transports along the ∼ 350 km length of

10 3 this shelf break sector amount to ∼ 1.75 350 ¼ 0.6 Sv on to the shelf in the

upper layers and off-shelf near the bed.

10.3.3 Cascading

It has long been suspected (Cooper and Vaux, 1949 ) that near-bed transport across
the slope in mid- and high latitudes may also be forced by density differences between
the shelf and slope produced by intensive cooling of shelf water during the winter
months. Because of the shallower depth, shelf water tends to cool more rapidly than
water over the slope and hence becomes denser than the slope water towards the end
of the winter cooling period. If the shelf water density exceeds that of the adjacent
slope by

D r, it will acquire a negative buoyancy b:

¼ ð shelf slope Þ
0

' g 0 : b g

0 g

¼ ð 10 : 16 Þ

Such dense water sitting at the top of the slope would be unstable and tend to flow
down the slope in an intense density current or cascade. The downslope flow will
be deflected by the Coriolis force and be diverted into an along-slope flow, but
frictional stress in the bottom boundary layer undermines geostrophy and ensures
that there will be a downslope component of flow even if bed topography is
uniform in the along-slope direction. Figure 10.8 illustrates the force balance for
steady flow of a layer of thickness h on a uniform slope with slope d relative to
horizontal. The downslope component of gravity, g 0 sin d, which is driving the
flow, is opposed by the frictional stresses F v and the Coriolis force. For the forces
acting in the plane of the slope, the balance in the direction of the flow can be
written as

g 0 sin sin ¼ F v ð 10 : 17 Þ

where y is the angle between the flow direction and the isobaths. In the direction
normal to the flow, the balance is given by:

g 0 sin ð f cos Þ V g ¼ cos ; ð 10 : 18 Þ