Mechanics of Lake Ice - Freezing of Lakes and the Evolution of their Ice Cover - page 148

es thermal cracks into dry, narrow and wide categories (see also
Ashton 1976). Dry cracks, which are the most common ones, do not penetrate the ice
sheet and act as bellows with temperature changes. Narrow wet cracks can freeze rapidly
and consequently add material to the ice sheet. Most of the contraction of an ice sheet is
concentrated at 1

Metge (1976) classi

2 wide cracks, which often form between two tensile stress risers, e.g.
between two headlands. They can be up to 20 cm wide (Metge 1976). In a long channel
they form at regular intervals, while other cracks skirt the shore from headland to head-
land. Wide cracks do not freeze through in one night but a thin ice bridge forms, and if the
daytime temperature is higher the bridges will break. This breakage is usually along shear
of inclined plane, and one side of the crack slips over the other that may initiate a pressure
ridge.
The rate of strain can be obtained from the temperature change as

-

e ¼ a T ð 5 : 17 Þ

where cient of linear thermal expansion. On the other hand, the relation

between strain-rate and stress can be taken as (Bergdahl and Wernersson 1978; Cox 1984)

ʱ is the coef

e ¼ 1

E r þ A r n

ð 5 : 18 Þ

Actual measurements of thermal pressure show magnitudes of 100 kN m − 1 .

5.2.4 Displacements in the Ice Cover

Occasionally shifts are observed in lake ice cover. They result from mechanical effects by
wind, water currents or gravity (lake surface tilt). Small displacements are also caused by
thermal expansion or contraction. These shifts can be detected by surface measurements,
and satellite SAR interferometry can be utilized to map two-dimensional small dis-
placements (see Dammert et al. 1998; Vincent et al. 2012).
The main forcing to break a lake ice cover comes from the wind. This is because a
strong wind blows in nearly the same direction across the lake, and wind stress ˄ a inte-

grated over a long fetch L grows into high level of forcing on the windward side of the
lake. There, at the shoreline the wind force is

˄ a L. The strength of the ice sheet is modelled
as P = P(h; l), where l is the length scale of ice stress. The strength represents the
integrated strength through the thickness of ice, and therefore its dimension is force/
length. The ice cover is stable as long as

s a L \ Ph ; ðÞ 5 : 19 Þ

100 kPa, has been used widely in sea ice
modelling (Hibler 1979). Then it is seen that at the limit of stability we have

A simple approach of P = P* h, P* 10

* -