Geoscience Reference
In-Depth Information
had an electric heating pad on one end of the bottom
with ambient fresh water in the tank. A layer of salt
water flowed along the bottom and over the heater. The
oscillation occurred because the layer of salt water sim-
ply spread over the heater and after some time interval it
mixed away. This was followed by another layer spreading
that was followed by mixing, repeating the cycle. The crite-
rion they found for oscillation is 0.038
< B
S
/B
T
<
0.067,
which differs from the criterion for the layered apparatus.
The first parameter is the buoyancy flux of heat,
B
T
=
gαF
T
WL/ρ
0
c
p
. The second is the buoyancy flux of salin-
ity,
B
S
=
gβS
0
q
.Here,
g
is the acceleration of gravity; heat
flux per unit area is
F
T
; the volume flux of salt solution is
q
; the box length is
L
; the box width is
W
; the reference
water density is
ρ
0
; the water's specific heat is
c
p
; and the
other symbols are previously defined.
Neither experiment produces clear evidence of the com-
plete criterion needed for oscillation. The balance is
clearly between the formation of a layer and its destruc-
tion from mixing along the interface, separating the layer
from ambient water. A simplified model of the oscillation
[
Whitehead et al.
, 2005] includes a freshwater layer that
deepens with time from interfacial mixing with salt water
below the layer. This is followed by complete mixing and
the start of a new layer at the top. It seems to produce the
effects observed in the laboratory (Figure 13.8).
0.8
T
0.4
0
-0.4
1−
S
-0.8
0
4000
8000
12,000
16,000
Time, (s)
Figure 13.7.
Density due to temperature and salinity versus
time for a little over two experimental oscillation cycles. The
top curve is from a temperature probe 2.54 cm below the top.
The density (from salinity of the water) is withdrawn at a depth
of 10 cm. The forcing strength is
−
αT
∗
/βS
0
= 0.85.
and the salt water below it decreases. Suddenly the bot-
tom layer's interface mixes away by direct overturning so
that the top layer lies over purely salt water (Figure 13.6c).
The cycle begins again as a new layer forms near the top.
A time series of temperature at a depth of 2.54 cm and
salinity at 10 cm depth is shown in Figure 13.7. The crite-
rion for oscillations is
13.4. SUMMARY AND DISCUSSION
Temperature-salinity abrupt transitions and oscillations
can be produced in the laboratory, as demonstrated by
four different experiments. It is necessary to precisely con-
trol all driving temperatures and pumping rates to hold the
experiment in the range of hysteresis. The findings gen-
erally confirm the presence of abrupt thermohaline tran-
sitions that were predicted by mathematical box models
−
∗
/βS
0
<
1.2. There is a small
range where this overlaps the steady temperature mode,
which is found for 1.15
<
αT
/βS
0
<
1.35.
The oscillation in the
Mullarney et al.
[2007] experiment
is similar to the above oscillation although their appara-
tus was inverted compared to the layered experiment. It
−
αT
∗
(a)
(b)
(c)
10
-3
10
-3
10
-3
×
×
×
2
T
T
T
2
0
10h
0
0
10
h
10
h
-2
-2
S
S
S
-2
-4
4
-4
-6
6
0
2
4
Time (s)
6
8
10
0
1
2
3
4
0
0.5
1
1.5
2
10
4
10
4
10
4
×
×
×
Time (s)
Time (s)
Figure 13.8.
Time series from numerical calculations of density from temperature and salinity, (given in the same units as in
Fig. 13.7) and layer depth
h
, (units multiplied by 10 and given in meters): (a)
−
αT
∗
/βS
0
= 0.5 (b)
−
αT
∗
/βS
0
= 0.85 (the value in
−
αT
∗
/βS
0
≤
Figure 13.7), (c
1.15. Adapted from
Whitehead et al.
[2005]).