ence as the intersection of two prismatic (rectangular) channels whose width greatly
exceeds their depth. For the moment, therefore, the influences of confluence mor-
phology (bars, islands, large dunes, rock outcrops, etc.) are not considered. Those
influences are discussed later, once the key nondimensional parameters are iden-
tified for characterizing flow and ice movement through a confluence of rectangu-
lar channels.
The analysis does not take into account the influences of engineered features
such as bridges, wharves, channel control structures, etc. The hydrologic influ-
ences of air temperature (as affecting freezing consolidation of drifting ice) and
wind also are neglected. While these structural and hydrologic factors are very
important, they do not play essential roles on ice movement through the conflu-
ence of prismatic channels, which is considered in the ensuing dimensional anal-
ysis. These approximations reduce the number of nondimensional parameters
needed to describe the essential processes that occur when two flows of ice merge.
Other, less significant simplifications are made subsequently in the analysis.
A further limitation of the ensuing dimensional analysis is the precise definition
of incipient jamming. The analysis assumes incipient jamming occurs when the
water and ice inflows to a confluence begin to exceed outflows of water and ice.
Actually, there probably are shades or degrees of incipient jamming. Outflows of
water and ice may be less than inflows and yet a jam may not have formed. Jam
formation is an unsteady, interactive process in which water and ice flows adjust
in accordance with, for example, changes in ice concentration and ice layer thick-
ness.
Categories of ice movement through confluences
It is helpful to categorize two conditions of ice movement through confluences:
A layer of drifting ice pieces with a velocity slightly less than that of the water
surface.
A thickened layer of ice extending approximately the full width of the channel
and moving with a velocity significantly less than the bulk velocity of water
flow in the channel.
Each category has several subcategories, in accordance with the combination of
ice discharge and water flow conditions in each confluent channel.
The distinction between drifting ice pieces and a moving layer of ice is useful,
because the forces propelling the ice into the confluence differ between the two
situations, and therefore differences arise between the sets of parameters needed
to describe the two categories. Flow drag and impact forces on individual ice pieces,
and the inertia of individual ice pieces, drive free-drifting ice pieces into a conflu-
ence. In contrast, boundary shear stress along the underside of an extensive accu-
mulation of ice, together with streamwise component of accumulation weight,
drive a moving accumulation of ice and possibly the momentum of the accumula-
tion. For free drift of ice, individual ice piece size is important. It is less important
in describing the behavior of an accumulation of ice, for which accumulation thick-
ness and width are more important.
In addition, it is likely that differences occur in the way the two categories of
confluent flows of ice merge. For example, significant shoving and thickening of
the confluent accumulations would accompany the merging of two moving par-
ticulate accumulations (category 2). Shoving and thickening would likely not
accompany the merging of confluent free-drifting ice pieces (category 1), at least
16
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