The shelf edge system - Introduction to the Physical and Biological Oceanography of Shelf Seas - page 306

Shelf Sea

Abyssal Ocean

Figure 10.2 The Taylor-Proudman theorem. The speed of the current may vary with depth but
the direction must be parallel to the isobaths at all levels. Notice that the current increases
where isobaths are closer together. Bathymetric steering of the flow acts to inhibit cross-slope
exchange. Deviations from isobath-parallel flow may occur due to (i) unsteady flow (e.g. in the
oscillatory tidal flow), (ii) energetic flow in which the Rossby number is large ( > 0.1) and (iii)
friction in the boundary layers.

Substituting in 10.4 and setting w ¼ 0 we have:

u
]

v u

]

u ] v ]

z þ z ¼ z ¼

ð : Þ

u 0 10 6

] ]

whichmeans that the velocity shear is parallel to the velocity, i.e. the flow direction is the same
at all levels and parallel to the isobaths, although the current speed may vary with depth.
This result, that the flow is topographically steered at all levels, constitutes a
fundamental constraint on steady geostrophic flow. Because of the particularly steep
topography over the continental slope, there is a strong tendency for this constraint
to operate there and for the flow to follow the bottom contours along the slope, as
illustrated in Fig. 10.2 . Notice how the flow speed increases where the isobaths are
closer together. Cross-isobath flow can only occur where one or more of the assump-
tions of the Taylor-Proudman theorem are broken and the flow is no longer geo-
strophic. This will be the case if (i) the flow is unsteady, or (ii) it is so vigorous that the
non-linear terms in the dynamical equation become significant and violate the
linearising assumption, or (iii) frictional effects are important as is the case in
the boundary layers near the surface and the seabed. 1

10.2.2 Slope currents

The dominating role of topographic steering is apparent in the pronounced 'slope
currents' which occur on many continental shelves and transport large volumes

1

In Chapter 3 we mentioned how the commonly held idea that the Gulf Stream bathes NW European
shelf seas in warm water is flawed because of the very weak mean flows seen in shelf seas. The
strong inhibition of cross-isobath flow in the Taylor-Proudman theorem provides another reason for
dispelling this misunderstanding.