Tidal mixing fronts: their location, dynamics and biological significance - Introduction to the Physical and Biological Oceanography of Shelf Seas - page 238

by stratification. As we mentioned in Section 6.1 , laboratory experiments on stirring
(Turner, 1973 ; Linden, 1979 ) suggest that mixing efficiency decreases rapidly as strati-
fication increases. This implies that, once stratification is established, it becomes harder
to break it down and re-establish vertical mixing. So after the advance of the front in
the period of weak stirring around neap tides, the efficiency of mixing is reduced in the
newly stratified area so that the retreat of the front towards the following spring tide is
reduced. This behaviour is also apparent in the seasonal cycle of stratification in the
shelf seas; following the initial onset of stratification in the spring, stability continues
to grow as the efficiency of mixing falls and robust stratification then continues
throughout the summer and persists until convective overturn begins in late summer
when surface heat exchange becomes negative (see Fig. 6.8a ). Only rarely is the cycle
re-started in the early weeks of stratification after an episode of strong mixing forces
complete breakdown of the initial stratification (e.g. Fig. 6.12 ).
A summary plot of frontal adjustment over the springs-neaps cycle based on
satellite I-R observations of frontal positions can be seen in Fig. 8.4 , which compares
the observed displacements of 400 frontal positions with theoretical models. The
movements of several fronts on the European shelf, after correction for tidal oscilla-
tion, have been combined by plotting in a non-dimensional form of h/u 3 against the
tidal range factor F which is the range of the tide divided by its value at neaps. The
F values plotted are those applying two days prior to the observed position, a lag
which gives the largest correlation between displacement and F. This lag indicates
that the maximum displacement of the front into stratified waters occurs not at
springs but

2 days later after a sustained period of higher than average stirring.
The form and magnitude of the small observed adjustment (

∼

2-4 km for typical
frontal gradients on the European shelf) is simulated reasonably well by models of

∼

5.5

4.5

3.5

2.5

1.5

0.5

0.8 1.2 1.6 2.0

F

Figure 8.4 Summary of observed spring-neap frontal displacement data plotted against the tidal
range factor F (F ¼ 1 at mean neap tides). Data are plotted in non-dimensional form as X/X m
where X ¼ h/u 3 is the value at the observed frontal position and X m is themean value for the frontal
position. The continuous curve represents the equilibrium adjustment. The open circle shows the
limit of adjustment over the fortnightly cycle when stored buoyancy is taken into account
( Equation (8.6) ) while the dotted curve is the result of model in which mixing efficiency varies with
stratification. Adapted from Simpson, 1981 , with permission from the Royal Society, London.