Geoscience Reference
In-Depth Information
Figure 7.6
Average values of (a)
dissipation
(a)
(b)
(Wm
3
) and the vertical
eddy diffusivity K
z
(m
2
s
1
), and (b)
the squared buoyancy frequency N
2
(s
2
) used to calculate K
z
(m
2
s
1
)
using the Osborn relation
Equation
(7.11)
.
e
N
2
10
-4
(s
-2
)
log
10
ε
(W m
-3
);
log
10
K
z
(m
2
s
-1
)
-5
-4
-3
-2
0
2
4
100
100
80
80
60
60
K
z
40
40
ε
20
20
0
0
water column during the midsummer period. If heat input to the bottom mixed layer
is only by downward diffusion, then we can write the heat balance as:
h
b
@
T
b
@
K
z
@
T
z
¼
N
2
@
e
T
t
¼
ð
7
:
12
Þ
@
@
z
@
T
where
@
z
is the temperature gradient in the pycnocline, h
b
is the thickness of the
bottom layer, and T
b
is the bottom layer temperature. If the density depends only on
temperature, then N
2
is the thermal expansion
coefficient. Substituting for N
2
, we have for the rate of temperature rise:
¼ð
g
=
0
Þ@=@
z
¼
g
@
T
=@
z where
a
@
T
b
@
e
t
¼
ð
7
:
13
Þ
g
h
b
which is, perhaps surprisingly, independent of the temperature gradient.
For e
10
7
Wkg
1
; h
b
¼
10
4
C
1
we find that:
¼
50 m;
G ¼
0.2; a
¼
1.6
@
T
b
@
10
7
Cs
1
65
C per month. This accounts for most of the observed
t
¼
2
:
5
¼
0
:
1
C per month, so we may reasonably conclude that the
observed dissipation in the pycnocline is a realistic measure of the vertical diffusion
which is driving fluxes of heat and nutrients and other properties through the pycnocline.
temperature rise of
∼
7.2.2
Physical mechanisms responsible for mixing at pycnoclines
What is missing in the physics of the TC model which causes it to fail in the pycnocline
region? There has to be one or more sources of energy for driving the weak internal
mixing observed. There are three main contenders for supplying this mixing, namely:
(i)
Internal wave motions
Large displacements of the isotherms are commonly observed to occur in the pycno-
cline as, for example, in
Fig. 7.5a
where there are variations of isotherm depths
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