Mechanics of Lake Ice - Freezing of Lakes and the Evolution of their Ice Cover - page 166

. When A < 1, lateral melting may
take place via absorption of solar radiation in open water patches. This can be added to
Eq. ( 5.44 ) in straightforward way by distributing the heat evenly to vertical

Here ice thinner than h 0 is accounted as ' open water '

floe surfaces

(see Rothrock 1986).

5.5.3 Static Ice Cover

Static ice cover is also termed as landfast ice. Stability was considered in Sect. 5.2.4
above. Now the question can be revisited based on the equation of motion. In the static
conditions,

u 0 , and, consequently,

rr þ s a þ s w q hg rn ¼ 0 ð 5 : 45 Þ

ed as long as the internal ice stress is beneath the yield level.
Consider the one-dimensional (x-axis) case, the lake located between x = 0 and
x = L. Integrating the static equation across the lake, we have

Stationarity is satis

Dr þ F ¼ 0 ; F ¼ s a þ s w ð Þ L q hg Dn ¼ 0 ð 5 : 46 Þ

where ' * '

stands for spatial averaging. In this case the ice cover can be viewed as an elastic-plastic
medium (Coon et al. 1974; Leppäranta and Wang 2008; Leppäranta 2011). To break the
ice, the integrated external forcing must reach the compressive strength P n h n (Eq. 5.36 )at
the windward side (Fig. 5.14 ). Equation ( 5.46 ) provides also a

ʔ refers to difference across the lake from x = L to origin, and the symbol

first approximation to two-
dimensional cases when L represents the fetch in the wind direction.

Fig. 5.14 Stability of lake ice at very strong winds. The lines show the breakage limit of ice
thickness as a function of fetch for ice strength linear and quadratic in ice thickness. The three
quadratic lines are set to agree with the linear case at ice thicknesses of 0.1, 0.3 and 0.5 m