Mechanics of Lake Ice - Freezing of Lakes and the Evolution of their Ice Cover - page 147

where M and n are in general functions of strain, strain-rate and stress, and D is the self-
diffusion coef

cient for the water molecules in ice. The parameter M shows a very large
variability in experimental data, and the coef cient D is given by

Q s
RT

D ¼ D 0 exp ð 5 : 16 Þ

9.1 × 10 − 4 m 2 s − 1 , Q s = 59.8 kJ mol − 1

where D 0 ≈ is the activation energy for self-

diffusion, R = 8.31 J mol − 1 K − 1 is the universal gas constant, and T is the absolute

temperature.

5.2.3 Thermal Cracking and Expansion

The thermal expansion coef cient of ice depends weakly on temperature. The linear

cient is 5.0 × 10 − 5 °C − 1 , i.e. 5.0 cm across 1 km distance for each one-degree
temperature change. It is clear that the strongest temperature variations take place near the
ice surface.
When the temperature changes fast, the elastic response dominates. In a cooling sit-
uation the surface ice contracts and tensile cracks are formed, while in warming the ice
cover expands. When the pressure is released by cracking, wave motion takes place in the
ice sheet and the crack propagation can also be heard. However, contraction and
expansion are not symmetric, since in the case of cracking, water comes up to

coef

ll the
cracks and freezes in. Then there is net expansion to spread the ice sheet further. In the
absence of snow, ice surface layer cools fast, and thermal cracking can be intensive
(Fig. 5.7 ). The temperature change is fast and large, so that the ice has not time enough for
viscous adjustment to the forcing.

(a)

(b)

Fig. 5.7 Schematic picture of thermal expansion (modified from Bergdahl 2002). a Right after a
rapid decrease in air temperature; and b Expansion of ice on a sloping shore, in mid-lake, and at a
straight shoreline