Mechanics of Lake Ice - Freezing of Lakes and the Evolution of their Ice Cover - page 168

dynamics before the year 2000. But much work was done for small marine basins, and
these models can be easily employed for lake research (e.g., Wang et al. 2003, 2006b;
Kubat et al. 2010). Recently, in Europe lake ice dynamics modelling work has continued
in Lake Peipsi (Wang et al. 2006a; Leppäranta and Wang 2008), and in North America
this work was restarted for the Great Lakes (Wang et al. 2010).
Table 5.3 shows the result of magnitude analysis of the terms of the equation of motion
based on the typical scales in lakes. Wind stress is the main driving force, largely com-
pensated by the internal friction of ice. Internal friction is strong due to the limited size of
lake basins with the presence of land boundary felt all over. The ice water stress, surface

-

pressure gradient and Coriolis acceleration have secondary in uences. In free drift of ice,

internal friction is zero and the wind stress must be compensated by ice

water stress and

-

surface pressure gradient. The inertia can become signi cant for very rapid changes in the

forcing. Advective acceleration is very small and will remain smaller than the ice - water

H/L C w , condition that is valid except for extremely exceptional

stress term as long as <

cases.
In the lake ice drift problem there are two principal time scales: local acceleration
T I = U/(C w H), and advection T D = L/U. Where Coriolis acceleration is signi cant, the

Coriolis period f - 1

also needs to be considered. These time scales are well separated,

T I << f - 1 << T D .
In free drift,byde . Since the momentum advection is very

small and T I < 1 h, an algebraic steady state equation results as a very good approxi-
mation. There are two speci

nition, we have rr 0

c classes of solutions (see Leppäranta 2011). If the Coriolis

acceleration is signi cant, we have

Fig. 5.15 The free drift
solution as the vector sum of
wind-driven ice drift and
geostrophic current (when the
Coriolis acceleration is
significant)

Wind

Wind-driven
component

Ice drift

Current velocity