2.4
baseline condition. The number of ice
calculation cycles for each water calcu-
Fully Coupled
2.2
lation cycle was set to 1. Another run was
made with the number of ice calculation
cycles set to 2. Figure 53 shows the final
2.0
jam thickness profiles for the fully
Uncoupled 2
Uncoupled 1
coupled and loosely coupled model
1.8
runs. The fully coupled model results
show a more pronounced effect of ice
1.6
0
1000
2000
3000
4000
5000
momentum. As the number of ice calcu-
x Location (m)
lation cycles increases, the resulting
Figure 53. Comparison of thickness profile
thickness profile attains a shape closer
predicted by loosely coupled model to fully
to the fully coupled thickness profile.
coupled model.
The minimal computational time saved
by using the loosely coupled model with
two or more ice calculation cycles is outweighed by the benefits of using a truly
fully coupled model.
Comparison with steady-state models
Steady-state models of jam thickness existed before high-performance mainframe
and personal computers became available. The computational power that exists
today allows very large coefficient matrices to be solved with little effort. The
execution time of the fully coupled model for tests similar to the baseline configu-
ration described in the Baseline Runs section is much less than the time required for
compilation of input files and analysis and plotting of output files. Even though
computational speed and capability have greatly increased, there still are reasons
(such as unsteady boundary condition information requirements) that a complex
model might not be used. For many situations, a steady-state model may be appro-
priate and provide results within a specified tolerance or accuracy desired. For
instance, Uzuner and Kennedy (1976) could formulate the upstream transition
region of jam thickness using a frame of reference that traveled upstream at the
speed of the progression of the jam front. The moving reference frame made the
flow quasi-steady and the computation much easier.
A widely used steady-state model for calculating water levels in ice-covered
channels is HEC-2 modified with the ice cover option or with the utility ICETHK,
or both. This model has been shown (Zufelt and Doe 1986) to yield accurate results,
provided the appropriate values of the jam-related variables are chosen. An impor-
tant input variable for a steady-state model is water discharge. However, ice jams
are markedly unsteady events characterized by widely fluctuating discharges: as
level ice covers (whence the jam ice originates) and ice jams fail, releasing stored
water, or as jams form, causing local reductions in discharge. A steady-state model
cannot account for local variations in discharge caused by jam formation or failure.
The discharge record shown in Figure 54 illustrates how unsteady flows can be
during jam breakup. Fortunately, the stage gauge used to estimate the discharges
in Figure 54 was located approximately 1 km downstream of the toe of the jam and
was ice-free during the event (except when the jam failed and ice passed down-
stream). The figure clearly shows when the jam initially formed, evidenced by a
drop in the discharge downstream at the gauge. It shows, too, the rise in discharge
as the water level in the jammed reach rose, and indicates the ultimate failure of the
jam, evidenced by the rapid peak and passage of the discharge wave. The local
69
Previous Page
