Mechanics of Lake Ice - Freezing of Lakes and the Evolution of their Ice Cover - page 167

Assume that n = 1. Then the aspect ratio h/L is the key dimensionless quantity of the
ice cover. For the ice cover to break, we must have

˄ a /P 1 > h/L. E.g., take P 1 * 30 kPa.

Wind stress for wind speed U a =10ms − 1 1 × 10 − 5 .In is ˄ a ≈ 0.3 Pa, and then, ˄ a /P 1 ≈

0.6 × 10 − 5 and the ice is mobile. In Lake Peipsi, L 50 km and when h 30 cm, h/L

* * *

a medium-size lake in southern Finland, L 40 cm, and the ice cover is

stationary. But with a major decrease in ice thickness and/or increase in wind speed the ice
cover can become mobile; very rare observations of modest ridging exist from the past in
mild winters but in general the ice cover is static. In spring, the ice cover rottens and the
strength decreases. Then ice cover may be displaced as sometimes seen as on-shore ride-
up or pile-up. However, the period of potential mobility is short and a considerable wind
speed is needed for displacements. It is known by experience in Finland that in some years
stable rottening takes place and in some years breakage and drift results.
In the ice strength law (Eq. 5.36 ), it seems that the power n should be more than 1. In a
study of landfast ice in the Baltic Sea, Leppäranta (2013) concluded that in the scales of
coastal basins n = 2 corresponded well to observations. Thus, if h

10 km and h

* *

* 0.3 m is the critical

thickness for lake size L 50 km, then for h 0.1 m and 1.0 it would be L 5 km and

* * *

L 500 km, respectively.

*

5.5.4 Models of Drift Ice Dynamics

When a lake ice-cover tends to break and the ice drifts, the ice appears as drift ice, and the
full dynamics equation (Eq. 5.42 ) provides the ice velocity solution. In spite of the
important role of ice mechanics in large lakes, very little research has been done in respect
of full thermal mechanical modelling. Continuum models were originally developed for

oceanic drift ice in the 1960s, but for lake ice they followed later. The

-

first efforts were
made in Soviet Union for the Caspian Sea (Ovsienko 1976) and in North America for the
Great Lakes (e.g. Wake and Rumer 1983). Thereafter, not much more was done in lake ice

Table 5.3 Scaling of the equation of motion of drift ice in lakes

Term Scale Value Comments

0.05 for rapid changes (T =10 3 s) Local acceleration ˁ HU/T <0.001

ˁ HU 2 /L

Advective acceleration <0.001 Long-term effects may be significant

Coriolis term ˁ HfU 0.005 Mostly <0.025

Internal friction PH/L 0 - 0.5 0 — open ice field, 0.5 — compact ice field

Air stress

q a C a U ag 2

0.2 Mostly significant

ˁ w C w U 2 0.01 May become 0.2 for open drift ice
Pressure gradient ˁ Hg ∇ʾ 0.005 Surface slopes limited in ice-covered basins
The representative elementary scales are: ice thickness H = ½ m, ice velocity U =10cms − 1 , ice
strength P = 50 kPa, wind velocity U a =10ms − 1 , water velocity U w = 0, lake surface slope
∇ʾ =10 − 6 , time T = 1 day, and horizontal length L = 50 km. The unit of “ Value ” column is Pa

Water stress