Distance Along River (m)
Figure 6. Comparison of water surface profiles.
Without bank friction
With bank friction
An analytical solution for the width-averaged ice
The steady-state ice thickness profile can be obtained
jam thickness profile can be derived by extending the
by simplifying the momentum equation, eq 22. When
only the water drag in x-direction, i.e., Fwx = ρcwVwx ,
solution of Pariset and Hausser (1961).
is considered and the bank friction is neglected, the ice
momentum equation is simplified to Rx + Fwx = 0. The
ti = teq (1 - e
(σ xx Nti ) +
(σ xy Nti ) =
( PNti ) . (49)
Using eq 37 for the pressure term leads to a simple
teq = (
analytical solution for the static ice accumulation
ti = (ti2
tan2 ( π + )(1 -
2 = N tanφ(1 + sinφ)
in which ti0 = single layer ice thickness and x = distance
1 = tanφ(1 sinφ) (Beltaos 1995)
from the leading edge of the jam where ti = ti0. The
simulated results and analytical solution are compared
in Figure 7. Figure 7a shows progressive thickening
φ = 46
and compressing of the simulated ice cover with time.
2 = 1.068
Figure 7b compares the analytical solution to the
1 = 0.29.
simulated ice thickness profile on and after t = 4 hours.
Table 1. Parameters used in the ice dynamic
Maximum ice concentration
Boundary friction coefficient
Water drag coefficient on ice