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Heat
(a)
0
u ( z , t )
t
Warm
t
Cool
Mixed
h
Cold
Tidal stirring
P T α u 3
h / u 3
Small
h / u 3
Large
(b)
0
115
13
10
-20
-40
°C
5 km
Figure 6.5 (a) A schematic illustration of the stratified and mixed regimes of a shelf sea, separated
by a tidal mixing front, from Simpson and James, 1986 , courtesy of the American Geophysical
Union; (b) a section of temperature observed across the tidal mixing front in the western Irish
Sea (Simpson, 1981 ), with permission from the Royal Society, London. The section in (b) was
collected using a towed, undulating CTD resulting in a horizontal resolution of 500 metres.
u 3 M2 . This prediction can be tested by examining the stratification of the shelf
seas using existing databases of temperature and salinity profiles to determine the
stratification parameter
value of h
=^
. An analysis of data for August from the shelf seas to the
west of the UK, shown in Fig. 6.6 , shows clearly the partitioning of the seas into
stratified (
F
up to 250 Jm 3 ) and mixed (
F
F
0) regimes separated by frontal boundar-
u s indicates that strong stratification is
ies. Comparison with the adjacent map of h
=
u s Þ >
associated with values of log 10 ð
1.5) correspond to com-
plete vertical mixing. The transitions between the two regimes, i.e. the tidal mixing
fronts, are seen to occur in all cases close to a value of log 10 h
h
=
3, while low values (
<
u s
9. This consist-
ency of the frontal positions, of which we shall hear more in Chapter 8 , provides strong
support for the idea that e
=
1
:
constant, at least in the region covered by Fig. 6.6 .
The mapping of the parameter h/u 3 has been undertaken for many regions of the
shelf seas worldwide using u from numerical models. As in the case of the European
shelf seas, a single value of h/u 3 appears to determine the positions of fronts in a given
region (Garrett et al., 1978 ; Lie, 1989 ; Glorioso and Flather, 1995 ; Kobayashi et al.,
2006 ) but there is some variation between regions in the critical value. This may be
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