length, or reduced jam strength), the jam eventually fails and moves downstream.
If an area of channel downstream is encountered where the resisting forces on the
moving ice are again great enough, the jam will reform. Existing models predict
the equilibrium jam thickness, which is the constant thickness that would be
expected in a uniform channel under conditions of steady flow when the resisting
and downstream-acting forces are perfectly in balance. Those models assume that,
when the net downstream-acting force reaches the level of passive pressure failure,
the jam must thicken to withstand the forces. The unsteadiness of both the ice and
water movement during a shoving and thickening event make the concept of equi-
librium thickness questionable.
In contrast with jam formation, juxtaposition (or surface assembly) of ice floes is
primarily a single-layer process that can be adequately described from hydraulics
considerations, and from the size, shape, and distribution of ice pieces. Much work
has addressed the problem of block underturning at the upstream edge of obstruc-
tions, and some work has addressed what happens to the blocks following
underturning. Such cover-formation processes are easy to visualize in the labora-
tory and the river, as they generally occur at the water surface and entail the
motion of single-layer ice floes coming into contact with a stationary obstruction.
The juxtaposition of ice floes or the motion of an ice block at the upstream edge of
an obstruction can be considered to be a fairly steady process because the effects of
ice-piece movement on the hydraulics are minimal.
Shoving and thickening, however, are much more common in nature during the
development of freezeup jams (made up of frazil slush or pans and small ice pieces),
as well as during the formation and evolution of breakup jams. The manner whereby
jams form and evolve is also important in determining how they fail. In compari-
son to the fairly steady water and ice motion during juxtaposition or underturning,
the ice and water interaction during jam failure and thickening results in highly
unsteady water and ice velocities, depths, and thicknesses.
REVIEW OF ICE JAM MODELING
It is convenient to review prior ice jam modeling in the context of the ways jams
develop and are classified. This section presents an ice jam classification system,
reviews past analyses of stationary jams, and briefly describes existing numerical
models used for predicting jam thickness.
Review of ice jam classification
The International Association for Hydraulic Research (IAHR) Working Group
on River Ice Hydraulics (IAHR 1986) published a state-of-the-art report classifying
the different types of ice jams and reviewing techniques for their analysis. The
report defines ice jams as stationary accumulations of fragmented or frazil ice that
restrict flow. This broad classification could include any form of ice cover or accu-
mulation, except for a thermally grown sheet ice cover. The classification system
distinguishes ice jams by their season of formation, dominant formation process,
spatial extent, and state of evolution. It is clear from the classification that jam for-
mation, whichever type of jam forms, is intrinsically unsteady. Jams develop and
adjust in thickness and extent in accordance with flow conditions, ice availability,
and weather conditions. Also clear from the report, however, is that existing for-
mulations of jams assume steady conditions, although unsteady water and ice move-