Tidal mixing fronts: their location, dynamics and biological significance - Introduction to the Physical and Biological Oceanography of Shelf Seas - page 241

@ v g

f @

z ¼

ð 8 : 7 Þ

@ @ x

where the x axis is in the cross frontal direction and the v velocity component is
parallel to the front. Equation (8.7) can be integrated upwards from the bed, where
we assume v

0, to determine the velocity field from density observations (e.g. see
Section 3.3.3 ). Using the density section across the western Irish Sea front, Fig. 8.5b
shows an example of the residual flow derived in this way. A relatively strong flow,
referred to as the frontal jet, is seen to be concentrated in the high gradient region
with a maximum speed of

¼

20 cm s 1 20 metres where the

horizontal density gradient changes sign. Notice that it is the strong gradients in the
lower part of the water column which make the larger contribution to the velocity
shear and are responsible for the rapid increase in speed with height above the bed.
This predominance of the gradients in the deeper water is commonly the case after
midsummer when the surface gradients tend to weaken.

located at a depth of

∼ ∼

Box 8.1 Geostrophic balance in a tidal mixing front

Tidal mixing fronts have a characteristic density field in which stratified water lies
adjacent to mixed water whose density is intermediate between the surface and
bottom layers in the stratified region. In the schematic plot of typical density
contours on a section normal to front shown in Fig. B8.1 , density in the surface
layers decreases in the x direction but this trend is reversed in the lower part of the
water column ( Fig. B8.1a ). These density changes give rise to pressure gradients
which are apparent in the slope of the isobars; isobars (dotted lines) have to be
farther apart where the density is lower. The sea surface itself is an isobar which
slopes towards the s tratified side of the front where sea surface elevation is lower by
an amount

h where

s

s and r m are depth-mean densities in the stratified
and mixed water respectively and h is the depth.

m

1

D

is usually, although not always,

positive (i.e. sea level is lower in stratified water); the density difference

¼ s m >

0 since the average temperature of the stratified water rises more
slowly than that of the mixed regime.
In a steady state without friction (the geostrophic balance), the pressure gradient is
balanced by the Coriolis force which acts at right angles to the flow ( Fig. B8.1b ) .
Hence the motion must be perpendicular to the pressure gradient and therefore
parallel to the front ( Fig. B8.1c ) . In the bottom layers, the isobars slope downwards
with increasing x. This implies a pressure force in the x direction which means the
force which acts at right angles to the flow must be directed out of the paper in
the negative y direction (for the northern hemisphere). With increasing height above
the bed, the slope of the isobars increases and, with it, the current speed until the level
of the pycnocline is reached. Further up the water column, the density gradient
reverses so that the slope of the isobars and the current speed are somewhat reduced