Geoscience Reference
In-Depth Information
The choice of u does not affect the shape of the contours of log
10
(h/u
3
) but does
change their numerical values and hence the critical value of log
10
(h/u
3
) at which
heating and stirring balance. A much-used map of the stratification parameter by
Pingree and Griffiths (Pingree and Griffiths,
1978
) for the European shelf uses
log
10
(h/k
b
u
3
)withh and u in cgs units and the drag coefficient k
b
¼
0.0025.
For the most widely used version of the h/u
3
parameter, we will use the shorthand form
Þ:
h
SH
¼
log
10
ð
=
^
u
3
with h (m) and uˆ (m s
1
).
6.1.3
Testing the stratification criterion using tidal mixing front positions
We shall consider the detailed physics of tidal mixing fronts and their importance
for biological processes in
Chapter 8
, but here we can use the observed positions of
fronts to test the theory of the previous section and, in the process, obtain an estimate
of the efficiency of mixing e.
The argument of the last section indicates that the shelf seas should be divided into
regions which exhibit seasonal stratification and others in which strong tidal stirring
rapidly mixes buoyancy inputs and maintains a vertically uniform water column.
This is shown schematically in
Fig. 6.5a
. Measurements of temperature and salinity
in summer along sections between areas of strong and weak stirring reveal this
transition from a single mixed layer to an approximately two-layer structure, as
illustrated, for example, by an early set of observations from the western Irish Sea
in
Fig. 6.5b
. This transition, which occurs rather rapidly, typically in a horizontal
distance
10km, is the tidal mixing front. For the example shown in
Fig. 6.5b
the
front occurs at a value of h
∼
220 m
2
s
3
. If we assume a typical summer heat
supply to the sea surface of the western Irish Sea of Q
i
¼
u
3
M2
=^
120 Wm
2
, and taking
10
4
C
1
, c
p
¼
10
3
Jkg
1
C
1
, r
0
¼
1026 kgm
3
, k
b
¼
10
3
,
a
¼
1.67
4.0
2.5
we can estimate the tidal mixing efficiency, e, by re-arranging
Equation (6.18)
:
3pag
Q
i
h
^
e
¼
0
:
0050
:
ð
6
:
19
Þ
8
0
c
p
k
b
u
3
M2
Rather surprisingly, this means that only
0.5% of the available stirring energy is
utilised in mixing; most of the energy input goes into heat, much of it in the highly
turbulent region near the bottom boundary. It is this concentration of turbulent
energy in the near bed region that accounts for the low efficiency of the mixing process.
In order to be effective in mixing, TKE needs to be injected close to the stable region of
the water column, i.e. in the vicinity of the pycnocline which, in the typical summer
scenario, is closer to the surface than the bottom as can be seen in
Fig. 6.5b
.
If our hypothesis of a constant efficiency of mixing is to be sustained, then we would
expect that all other frontal transitions in adjacent areas should occur at the same critical
∼
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