Estimation of dividing streamline position
Based on the foregoing method of estimating the extent of the separation zone,
an approximate estimation is possible of the position of the dividing streamline
that delineates flows merging from channels 1 and 2. If constant depth is assumed
through the confluence, the dividing streamline location is proportional to the
discharges of the contributing channels; i.e.,
b3 - bd Q1
=
(5)
bd - bs Q2
whence
Q1bs + Q2b3
bd =
Q1 + Q2 .
(6)
These equations, together with eq 4, can be used to estimate the approximate width
of channel occupied by each merging ice run.
Bathymetry of concordant bed confluences
The confluence flow studies mentioned above deal with confluent channels of
relatively simple geometry, usually rectangular and flat bottomed. The bathyme-
try of actual river confluences is not so simple, as Figures 4b and 5b illustrate for
concordant bed and discordant bed confluences. The present section focuses on
the bathymetry of concordant bed confluences, as is fairly typical of the conflu-
ence of more or less similar size channels, such as the confluence of the Missouri
and Mississippi Rivers.
The bathymetry of concordant bed confluences includes zones of sediment scour
and sediment deposition. The zones reflect regions of greater or reduced flow
velocity. Best (1988) and Biron et al. (1996) provide useful descriptions of the
bathymetry of concordant bed channels. Their descriptions are based on laborato-
ry flume experiments and field observations.
An important bathymetric feature is the zone or line of maximum scour, whose
position is closely related (if not identical) to the position of the dividing stream-
line. Figure 7 indicates the approximate relationship between the orientation of
the line of maximum scour depth, βs, and the apex angle of confluence, α, for
several discharge ratios, Qr = Q1/Q2. One aspect of bathymetry that is not included
in the descriptions published to date is the formation of a large dune at the down-
stream end of the scour region. Such a dune, perhaps termed a mega-dune,
appears to form at the confluence of the Mississippi and Missouri Rivers.
It is very common for a portion of sediment transported into a confluence of
concordant bed channels to become entrapped and accumulate within the flow
separation zone. The accumulating sediment builds out as a bar that attains an
equilibrium extent coinciding minimally with the extent of the average flow sepa-
ration zone developed for the annual average discharge through the confluence.
In actuality, the bar may oscillate in extent throughout a year, varying in concert
with the magnitudes of inflow into the confluence. There appears to be little infor-
mation published on the variation of bar size with flow conditions and overall
confluence geometry. Additionally, bars may become stabilized by means of veg-
etation growth and tend to continually build outwards into the confluence. In so
doing, they force the confluence outflow channel to shift laterally in a manner
somewhat similar to the migration of meander bends in rivers.
14
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