Tidal mixing fronts: their location, dynamics and biological significance - Introduction to the Physical and Biological Oceanography of Shelf Seas - page 265

where z is the vertical density gradient and L is the horizontal displacement

of the particles. Hence show that the maximum energy release occurs when

@ r/ @

1
2 tan

tan ¼

i.e. when the particles are exchanged along surfaces with half the slope of the
isopycnals.
8.4. Satellite I-R data indicate that the displacement of TM fronts over the springs-
neaps cycle corresponds to a change in the tidal mixing parameter of

0.25. Use this information to determine the ratio of the amplitudes of the M 2
tidal stream at the extremes of the displacement cycle of a front occurring in a
region of uniform bottom depth (h

D SH

constant). Hence estimate the extent of the
displacement of the front in kilometres if the M 2 tidal stream amplitude u M2
varies as u M2 ¼

¼

gx) where x is the distance normal to the front, u s is the
amplitude at the position of the front following springs where x

u s (1 þ

¼ 0 and the

10 5 m 1 .

constant g ¼ 9

8.5. Just after spring tides, the surface water on the mixed side of a TM front is found
to have a nitrate concentration of 1 mmol m 3 . Noting any assumptions that
you make, estimate:

(i) The mean rate of primary production (g C m 2 d 1 ) supported by the spring-
neap frontal adjustment.
(ii) The contribution to the annual phytoplankton carbon fixation (g C m 2 a 1 )
made by the spring-neap adjustment.

8.6. Treat the instability scale at the front in Problem 8.1 as an estimate of the eddy
size.

If the mixed water has a nitrate concentration of 2 mmol m 3 , estimate the total
carbon that could be fixed when the eddy transfers nitrate into the stratified side
of the front.