Geoscience Reference
In-Depth Information
ows under ice cover and their effect on the circulation was
given by Bengtsson (1996). These effects are usually localized near in- and outlets; they
affect the ice thickness, especially near the inlets, and they may alter the vertical strati-
A review of the river in
fl
fication near the outlets by selective water withdrawal (Stigebrandt 1978). In small lakes,
in
ows can initiate a secondary, lake-wide, geostrophic circulation (Svensson and Larsson
1980). In deep lakes, in
fl
ows play an important role in the lake-wide lateral circulation and
the deep-water formation. Hohmann et al. (1997) suggested that the in
fl
ow of River
Selenga in Lake Baikal plunges down and initiates a thermobaric instability (see
Sect.
7.1
), which mixes the water column down to the lake bottom
fl
—
the crucial process
for the ventilation of the deep waters.
7.2.2 Stratification
The initial temperature conditions at the freeze-up are created in the autumn mixing and
therefore then T
≤
T
m
. The temperature at the ice
-
water interface is at the freezing point,
T
0
= T
f
, and if T
m
> T
f
, inverse thermal strati
cation forms. In freshwater lakes the upper
layer temperature is close to the freezing point, T
1
≥
T
0
and the lower layer temperature is
between the freezing point and the temperature of maximum density. Thus
T
f
T
1
T
2
T
m
ð
:
Þ
7
18
On top of the upper layer, just beneath the ice, there is a thin surface layer where
diffusion is molecular and the temperature increases from T
f
to T
1
. In fresh-water lakes, we
can take T
f
=0
C. If the concentration of dissolved matter increases in the
bottom water due to dissolution from the sediments, a thin bottom layer is formed into the
lower layer (e.g., Malm 1998).
The stability of temperature strati
°
C and T
m
=4
°
cation is described by the Rayleigh number:
Ra ¼
g
a
D
Td
3
jm
ð
7
:
19
Þ
where
ʱ
is thermal expansion coef
cient,
ʔ
T is the temperature change across the layer of
10
−
6
m
2
s
−
1
is
the viscosity. Rayleigh number may be taken as the ratio of buoyant and viscous forces.
When Rayleigh number exceeds a critical value of
10
−
7
m
2
s
−
1
is the thermal diffusivity, and
thickness d,
ʺ
= 1.3
×
ʽ
= 1.8
×
10
3
, convection starts up. This may
*
bring heat to the ice bottom.
Example 7.5
. Assume that the temperature of the upper layer is 5
°
C. Cooling the surface
to 4
°
C leads to molecular diffusion with the thickness of the cold layer increasing as
t)
1/2
(see, e.g., Thorpe 2005). The Rayleigh number then grows proportional to
time to the power of 3/2 and reaches the critical value. Since
ʴ
=(
ˀʺ
10
−
4
C
−
1
, Ra
ʱ
* -
¼×
°
reaches the critical limit of 10
3
in 4 min.
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