Page 90 - Fundamentals of Geomorphology

GEOMORPHIC MATERIALS AND PROCESSES 73

half the product of mass and velocity, so for a stream expressed in the oft-reproduced Hjulstrøm diagram
it may be defined as (Figure 3.11), cover a wide range of grain sizes and flow
velocities. The upper curve is a band showing the criti-
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E k = mv /2 cal velocities at which grains of a given size start to erode.
The curve is a band rather than a single line because
where m is the mass of water and v is the flow velocity. the critical velocity depends partly on the position of the
If Chézy’s equation (p. 71) is substituted for velocity, the grains and the way that they lie on the bed. Notice
equation reads that medium sand (0.25–0.5 mm) is eroded at the low-
est velocities. Clay and silt particles, even though they
E k = (mCRs)/2 are smaller than sand particles, require a higher velocity
for erosion to occur because they lie within the bottom
This equation shows that kinetic energy in a stream is zone of laminar flow and, in the case of clay particles,
directly proportional to the product of the hydraulic because of the cohesive forces holding them together.
radius, R (which is virtually the same as depth in large The lower curve in the Hjulstrøm diagram shows the
rivers), and the stream gradient, s. In short, the deeper velocity at which particles already in motion cannot be
and faster a stream, the greater its kinetic energy and transported further and fall to the channel bed. This is
the larger its potential to erode. The equation also con- called the fall velocity. It depends not just on grain size
forms to the DuBoys equation defining the shear stress but on density and shape, too, as well as on the vis-
or tractive force, τ (tau), on a channel bed: cosity and density of the water. Interestingly, because
the viscosity and density of the water change with the
τ = γ ds amount of sediment the stream carries, the relationship
between flow velocity and deposition is complicated. As
where γ (gamma) is the specific weight of the water the flow velocity reduces, so the coarser grains start to fall
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(g/cm ), d is water depth (cm), and s is the stream out, while the finer grains remain in motion. The result
gradient expressed as a tangent of the slope angle. is differential settling and sediment sorting. Clay and
A stream’s ability to set a pebble in motion – its silt particles stay in suspension at velocities of 1–2 cm/s,
competence – is largely determined by the product of which explains why suspended load deposits are not
depth and slope (or the square of its velocity). It can dumped on streambeds. The region between the lower
move a pebble of mass m when the shear force it creates curve and the upper band defines the velocities at which
is equal to or exceeds the critical shear force necessary for particles of different sizes are transported. The wider the
the movement of the pebble, which is determined by the gap between the upper and lower lines, the more con-
mass, shape, and position of the pebble in relation to tinuous the transport. Notice that the gap for particles
the current. The pebbles in gravel bars often develop an larger than 2 mm is small. In consequence, a piece of
imbricated structure (overlapping like tiles on a roof), gravel eroded at just above the critical velocity will be
which is particularly resistant to erosion. In an imbri- deposited as soon as it arrives in a region of slightly lower
cated structure, the pebbles have their long axes lying velocity, which is likely to lie near the point of erosion. As
across the flow direction and their second-longest axes a rule of thumb, the flow velocity at which erosion starts
aligned parallel to the flow direction and angled down for grains larger than 0.5 mm is roughly proportional to
upstream. Consequently, each pebble is protected by its the square root of the grain size. Or, to put it another
neighbouring upstream pebble. Only if a high discharge way, the maximum grain size eroded is proportional to
occurs are the pebbles set in motion again. the square of the flow velocity.
A series of experiments enabled Filip Hjulstrøm The Hjulstrøm diagram applies only to erosion, trans-
(1935) to establish relationships between a stream’s flow port, and deposition in alluvial channels. In bedrock
velocity and its ability to erode and transport grains of a channels, the bed load abrades the rock floor and causes
particular size.The relationships, which are conveniently vertical erosion. Where a stationary eddy forms, a small