Tidal mixing fronts: their location, dynamics and biological significance - Introduction to the Physical and Biological Oceanography of Shelf Seas - page 247

gradient of tidal stirring at a front inhibits the growth of instabilities, but although
there are a number of suggestive cases (e.g. the stable Islay front (Simpson et al.,
1979 )), this idea remains a hypothesis to be tested. Where eddies do occur regularly,
they clearly dominate the frontal zone and make a substantial contribution to the
transfer of properties across the front.

8.5 Transverse circulation

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Where fronts are not subject to frequent instability, we may still regard the front
dynamically as having an approximately 2D, geostrophically balanced flow along the
front direction. In the ideal frictionless case there will be no component of current
normal to the front. In reality, friction will lead to some cross-frontal exchange.
Including the frictional stresses in the equation of motion, we have the steady state
version of Equation (3.13) with no external forces:

1 @ p

x þ @

t x
@

1 @ p

y þ @

t y
@

fv ¼ ; fu ¼ : ð 8 : 9 Þ

@ z @ z

Frictional stresses arise in the shear flow associated with the baroclinic jet and
modify the along-front flow so that the geostrophic balance is no longer exact. The
unbalanced component of the pressure gradient then acts to drive an ageostrophic
component of flow normal to the front. Assuming the stresses are related to the
velocity shear by a known eddy viscosity ( Equation 3.32 ), the dynamical Equations
( 8.9 ) together with the continuity Equation (3.1) may be solved numerically for
a given density distribution to determine the frontal flow. For realistic friction,
the along-front jet is only slightly modified but friction does induce a significant
cross-frontal circulation (James, 1978 ; Garrett and Loder, 1981 ). In Fig. 8.10 you can
see an example, based on a model, of the circulation for the tidal mixing front at the
edge of Georges Bank which shows two contra-rotating circulation cells combining
to form a downwelling flow with a surface convergence and an upwelling movement
in the mixed water close to the bank.
There is some evidence for both of these features occurring in fronts. Accumulations
of surface-active material 2 and flotsam along lines parallel to the front are frequently
observed in frontal zones in, or close to, the region of largest surface gradients,
indicating a convergence of flow. At the same time, a slight minimum in surface
temperature, which is often observed on frontal crossings at a point just prior to the
sharp temperature rise (see Fig 6.5b for an example), suggests the influence of cold
water upwelled from the lower layers of the stratified system. The direct measurement
of these cross-frontal flows, which have magnitudes

1cms 1 , poses a formidable
challenge but the results from some dye tracer experiments (Chen et al., 2008 ) provide
further support for our conceptual picture of cross-frontal circulation.

∼

2 Surface active material refers to organic substances in a thin surface microlayer which reduces
surface tension and damps capillary waves, often creating a visible slick.