
StDIMfNT TRANSPORT BY UNIDIRFC TIONAL WATl-.R nCAVS
611
the boundary grain Reynolds number is proportional to the
ratio of grain diameter/thickness ol'the viscous sublayer. For
Reh less than 5 to 10 (hydratilieally smooth flow), the grains
are immersed in the viscous sublayer, are subjected mainty to
viscous forces, and are sheltered frotn the much greater drag
forces of the turbulent flow above. This is the reason why the
dimensionless bed shear stress must be relatively large to
entrain these grains (Figure S^). However, this is also partly to
do with inereasing effects of cohesion in very small grains. If
bed grains project high above the viscous sublayer {Reh>10 to
100:
hydrauliealiy rough flow), turbulent shear stresses and
form drag are dominant, viseous forces are negligible, and the
threshold of motion beeotnes independent of Reynolds
number (Figure S9). For fixed values of fluid and sediment
density, the threshold ol entrainment can be expressed in terms
of bed shear stress and graiu si/e (Figure S91,
The threshold
oi"
motion shown in Figure S9 is eoniposed of
il range of experimentally determined values. This range exists
partly because not all of the controlling parameters {sueh as
bed slope and relative size, shape and arrangement of grains on
the bed) are represented on plots of dimensionless bed shear
stress ;iiid boundary grain Reynolds number. However,
perhaps the main reason for the range is the difficulty in
defining the threshold of motion. Turbulent flow is assoeiated
wilh fluid drag and lift forces that vary greatly in titne and
space. These forces are acting upon grains that vary in size,
shape, and arrangement on the bed. Thus, a locally high
instantaneous fluid foree may dislodge a few ofthe most easily
nuned grains, but may not produce general sustained move-
ment. Such intermittent movement may be difflciilt to observe
(sec Grain Threshold).
The threshold of motion detined in Figure S9 only applies to
planar beds with relatively small slopes. Some theories take
mto account the effeets of bed slope (e.g., Wiberg and Smith.
19S7;
Bridge and Bennett. 1992). If there are bed waves such as
ripples or dunes present on the bed, the threshold of motion is
complicated by non-negligible bed slope and the faet that the
spatially ;i\eraged bed shear stress includes components of
bed-form drag thai do not effectively act on bed grains. Thus,
ill order to define the threshold of motion tin bed waves, it is
necessary to define loeal fluid drag and lift on their upstream
sides,
and lo aeeount for the upstream sloping bed surfaee.
The threshold of motion delincd in t igure S9 only applies to
the mean grain size of grains that do not vary much in size,
shape, and density. Prediction ofthe threshold of entrainment
of individual grains in a mixture of grains of different si/e.
shape, and density requires much more detailed analysis of the
forees involved, ineluding turbulent variations in fluid drag
and lift. There are a number of dilTerent theoretical and
empirical approaches to this problem (reviews by Bridge and
Bennett, 1992: Komar, 1996; Buffington and Montgomery.
1997;
Bridge. 2003). All ofthe approaehes predict that the
threshold of motion for a particular grain size in the mixture
depends on its size relative to the median size ofthe mixture.
Larger-than-average grains are relatively easier to entrain than
il ali grains were the same size, whereas the opposite is true lor
the smaller-than-avcrage grains. This is because large grains
protrude relatively higher into the llou where average fluid
velocity is greater, and because friction angles are relatively
lou. Such grains may have dimensionless bed shear stress as
low as 0,01 at the threshold of motion. In contrast, small
grains sit low in the flow and have large friction angles, or are
hidden by the larger grains. In rare cases, the threshold of
motion of the large and small grains may be so similar that
they are almost equally mobile. However, these predictions are
based on consideration of timc-avcraged fluid drag and lift, lt
is important to consider turhulettt variations in fluid drag and
lift, as these cause different fractions to move at different
times.
Small grains may not actually be hidden from turbulent
lift associated with flow separation to the lee of larger grains.
The largest grains may only move under the influence of the
largest instantaneous fluid drag or lift, and not by the mean
values. Lack of consideration of turbulenee may lead to
underestimation ofthe threshold shear stresses for the larger
grains, and vice versa for small grains.
In view of the fact that fluid turbulence has a dominating
influence on sediment entrainment, and that turbulent motions
vary in time and spaee. it is not surprising that when a
particular size fraction starts to move on the bed. not all ofthe
grains of that size fraetion on the bed will be moving. This will
be particularly true for the coarsest fractions that require the
largest instantaneous turbulent stresses for movement. The
condition where some ofthe grains ofa given size on the bed
move wilhin a given time interval, but not all of them move,
has been called partial transport by Wilcock and McArdell
(1997),
Partial transport is thought to be common in many
gravel-bed rivers. As would be expected, the proportion of
grains present in the bed that are mobile is greatest for the
finest sizes and least for the coarsest sizes.
The threshold of transport of
cohesive sediment (mud)
Cohesion in muds is the dominant eontrol on resistanee to
entrainment (review by Black
etaf,.
2002). Cohesion is partly
due to eleetro-chemical forces, the magnitude of which
depends on mineralogy (e.g.. exchangeable cations), the size,
shape, and spatial arrangement of the elay flakes, and ihe ionic
properties of the pore water and eroding water. However,
cohesion can also be due to microbial organistns (bacteria,
microphytobenthos). Resistanee properties also depend on the
state and history of et>nsolidation. For example, there may be
a flocculated structure, a pelleted structure due to desiccation
and bioturbation, or fissility due to compaction. Certainly,
eompacted and dry clays are more difficult to erode than soft,
wet clays. Many experimental studies have been eonductcd to
establish relationships between critical bed shear stress for
entrainment and some gross property of the clay sueh as
eohesive shear strength, liquid and plastic limits, percent elay,
density, permeability and porosity. These parameters have
usually been linked to critical shear stress one or two at a time
using only one type of clay-water complex. There are no
universal correlations for all types of clays in all aqueous
environments. The nature of entrainment also depends on the
state and history of eonsolidation. which will determine
whether the clay is eroded as individual flakes, floccules, or
fragments of consolidated mud. Also, direet fluid stress may be
augmented by impacts on the bed of grains already in motion.
Bed load
Sediment grains with diameters greater thau approximately
0.1 mm (sand and gravel) generally move close to the boundary
(within ten grain diameters) by rolling, sliding and saltating
(jumping). These grains move more slowly than the surround-
ing fluid because of their intermittent collisions with the bed