Tidal mixing fronts: their location, dynamics and biological significance - Introduction to the Physical and Biological Oceanography of Shelf Seas - page 264

(Hint: From the figure estimate the horizontal gradient of density above and
below a depth of 30 m. Use these values with the thermal wind equation to
determine the vertical shear and hence the current profile.)

z

A

0 metres

25.2 25.4

25.0

-40

25.8 25.6

26.0

-80

0 10 20 30 km

8.2. In a shelf sea region, where stirring is mainly due to tidal forcing, the potential
energy anomaly

h/u 3 and the time F (y, t) can be represented as a function of y ¼

F 0 (t) is the corres-

t which has elapsed since the spring equinox (March 21). If

ponding value of which would occur in the absence of stirring, show that the

efficiency of mixing e can generally be expressed as

F

y ð 0 Þ

C d

e ¼

t

where k is the drag coefficient. Hence, show that e can be related to its value e f at
a TM front where y

¼ y f and F ! 0by:

y
y f :

e
e f ¼ 0

1

205 J m 3 , observations showed that 185 J m 3 at On June 30, when F 0 (t) ¼ F ¼

2100 m 2 s 3 . Compare the value of e at the
stratified site with that at the front where y f ¼

a stratified position where y ¼

400 m 2 s 3 and suggest an

explanation of your result.
(Hint: Start from an integrated form of the

F equation (e.g. 6.24 ) and discount

1026 kg m 3 .) wind stirring. Use C d ¼ 0.0025 and r ¼

8.3. The kinetic energy input to baroclinic instability of fronts comes from the
release of potential energy from the density field by the exchange of water
particles across the front. In a section normal to a front, the isopycnals slope
uniformly at an angle b to the horizontal. Show that the energy released by
exchanging two particles of unit volume along paths inclined at an angle y is
given by:

¼ @
@ z gL 2 tan

ð Þ

PE tan tan