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where Q b is the heat
fl
flux from lake bottom, and
ʓ H is the in
fl
uence of horizontal advection
and diffusion.
7.1.2 Two-Dimensional Features in Pre-winter
The progress of the pre-winter also contains two-dimensional features, apart from the
in
uence of general circulation. Cooling of water is naturally fastest in shallow areas, in
particular in the near-shore zone, and extends offshore. At T 0 > T m , cooling nearshore
waters become denser, sink, and
fl
fl
flow toward deeper parts along the sloping bottom.
Central basin surface waters
flow laterally toward shore to close the loop. Even in
medium-size lakes the deep basin may freeze several weeks later depending on the
weather conditions. In deep lakes, mixing with no freeze-up may continue through the
winter; in limnology they are called warm monomictic lakes (Hutchinson 1957).
The situation T 0 < T m is
fl
first reached near the shoreline. Then the thermohaline cir-
culation system becomes blocked at the shore, and the 4
C isotherm is shifted further
offshore (Fig. 7.3 ), and as a result the freezing of the central lake is delayed. The blocking
4
°
°
C isotherm is called thermal bar (Zilitinkievich et al. 1992). In principle it is present in
all lakes but in large lakes the time scale of the thermal bar lifetime becomes long.
Example thermal bar is regularly observed in Lake Ladoga, the largest lake in Europe,
where it persists for several weeks (e.g., Rumyantsev et al. 1999).
7.1.3 Analytic Slab Models
Analytical modelling of the cooling process is based on Eq. ( 7.7 ). Approximating the
water temperature to be vertically uniform, we have a one-layer equation, called the slab
model. The linearized form (Eq. 4.20 ) is employed for the atmospheric and solar heat
fl
ux
to the lake. Then Eq. ( 7.7 ) becomes:
Fig. 7.3 Thermal bar in Lake
Ladoga (redrawn from
Melentyev et al. 1997). The
4 ° C isotherm separates the
circulation from coastal and
central parts of the lake for
longer periods
River
Volkhov
4°C
4°C 3°C 2°C
0
20
6°C
5°C
40
60
100 km
 
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