Mechanics of Lake Ice - Freezing of Lakes and the Evolution of their Ice Cover - page 169

u ¼ u a þ U wg ð 5 : 45a Þ

where u a is the wind-driven velocity and U wg is geostrophic current velocity: The wind-
driven part is given by the wind factor u a /U a ≈

2.5 % and the deviation angle, which tells

that the direction of ice drift is about 10 30° to the right (northern hemisphere) or left

(southern hemisphere) from the wind (Fig. 5.15 ). When the Coriolis acceleration is not
signi

-

cant, we have

s

q a C a
q w C w

q
q a C a gh rn

u ¼ jj ; W ¼ U a U a ð 5 : 45b Þ

and the direction of ice drift follows the direction of the vector W .
In compact ice, the forcing needs to be strong enough to break the yield criterion. The
ice starts motion, and the importance of the internal friction is then described by the
friction number

X ¼ P ð H Þ
FL

ð 5 : 46 Þ

The ice rheology has a distinct asymmetry: during closing the stress may be very high
but during opening it is nearly zero. In a channel with closed end the full steady state
solution is a stationary ice

field with a very sharp ice edge. In the spin-down the ice ows

as long as the forcing overcomes the yield level ( < 1).

In general, in the presence of internal friction the ice drift problem is solved using
numerical models. The one-dimensional channel case can be treated semi-analytically,
and the solution provides a good insight into the role of internal friction. The channel is
aligned along the x-axis and closed at x = L (Fig. 5.16 ). The boundary conditions are u =0
at x = L and

X

flow is examined using the quasi-
steady-state momentum equation and the two-level ice state

σ = 0 at the free ice edge. The channel

J ={ h , A }. The system of

equations is then written as:

o r
o x þ s a þ q w C w U w u

j j U w u ð Þ q gh rn ¼ 0 ð 5 : 47a Þ

Fig. 5.16 The geometry of the
channel flow problem