The shelf edge system - Introduction to the Physical and Biological Oceanography of Shelf Seas - page 320

flow involves large radial accelerations. A useful criterion for the breakdown of
geostrophy in this way is based on the Rossby number, RN, which represents the
ratio of inertial and Coriolis forces. Flow is judged to deviate significantly from
geostrophy when

V
fL >

RN ¼ 0 : 1 ð 10 : 20 Þ

where V and L are velocity and length scales characterising the flow. High Rossby
number flow can result in incursions of the slope current on to the shelf as, for
example, in the deflection of the Kuroshio into the Sea of Japan and the East China
Sea by a tight bend in the topography where RN 0.3 (Hsueh et al., 1996 ). Irregular-

ities in the topography can also generate eddies and meanders and, hence, increase
cross-frontal transfer. Such influence is exemplified by the effect of a pronounced
topographic feature, the Charleston Bump, in promoting cross-stream perturbations
in the Gulf Stream as it flows as the slope current along the south and mid-Atlantic
Bight of eastern North America (Oey et al., 1992 ;Miller, 1994 ).

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10.4 The internal tide

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Cross-slope flow can occur when the time scale of the motion means it cannot be
regarded as steady. The oscillatory motions of the tides are an important case of such
unsteady motion. The barotropic tide, which originates in the deep ocean and flows
onto and off the shelf every tidal cycle, varies sufficiently rapidly to be exempt from
the geostrophic constraint. The motion is reciprocating so it does not involve direct
volume transport across the slope, but in stratified waters these barotropic tidal flows
can lead to large internal tidal waves travelling along the pycnocline. These internal
tidal waves propagating onto continental shelves can often generate substantial
turbulence and thus promote vertical mixing. In combination with these mixing
processes, which are irreversible, tidal flow may result in some net transport of scalar
properties across the slope. Another cross-slope transport mechanism due the
internal tides results from solibores, non-linear internal waves, which are a by-
product of the internal tide. We will next examine in some detail the processes
involved in the generation of the internal tide and the associated wave motions.

10.4.1 Generation of internal motions

The generation of the internal tide at the edge of the continental shelves is a globally
ubiquitous phenomenon with important implications for the biogeochemistry.
Energy is fed into the internal tide by the interaction of the barotropic tidal flow
over the slope with water column stratification. The essential mechanism, which is
illustrated for uniform two-layer stratification in Fig. 10.11 , involves the displace-
ment of the stratified water column up and down a steep slope. During the flood,