Rivers & Streams:
Sedimentation and Erosion
Benoit Cushman-Roisin
New dam and reservoir as
designed and planned What happened later contrary to plan
The largest river on the planet, the Amazon, forms from the confluence of the Solimões (the upper Amazon River) and the Negro at the Brazilian city of Manaus in central Amazonas. At the river conjunction, the muddy, tan-colored waters of the Solimões meet the "black" water of the Negro River. The unique mixing zone where the waters meet extends downstream through the rainforest for hundreds of miles, and attracts tourists from all over the world.
It is the vast quantity of sediment eroded from the Andes Mountains that gives the Solimões its tan color. By comparison, water in the Negro derives from the low jungles where reduced physical erosion of rock precludes mud entering the river. In place of sediment, organic matter from the forest floor stains the river the color of black tea.
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Apparent weight
Almost all sediment particles regardless of size have a density equal to
s= 2,650 kg/m3.From this, one defines the specific gravity, which is the ratio to the water density:
65 . 000 2 , 1
650 ,
2
s sWeight of particles
Assuming spherical particles of diameter ds, we have:
Volume:
Weight: 3
3
6 6
s s s s
s s
gd g m F
d V
Apparent weight (net weight) = actual weight minus buoyancy force
3
3 ( 1)
) 6
6( s s s
b
s F gd s gd
F
F
Settling speed
The settling speed, also called terminal fall velocity, is the speed acquired by a falling sediment particle when its downward apparent weight is balanced by the upward drag force due to the movement with respect to the water.
Drag force is:
The balance of forces yields:
2
2 2
1 1
2 2 4
s
d D s s D s
F CA w Cd w
2
2 3
1 ( 1)
2 4 6
( 1)4 3
s
d D s s
s s
D
F F C d w s gd
w s gd C
Problem is that CDvaries
with speed and size!
Erosion
A particle on top of the bed will be entrained into the flow if - its center of gravity is vertically above the points of contact,
- lift and drag forces combine into a force capable of pivoting the particle upward at the downstream point of contact.
Note: If the sediment is cohesive, a cohesion force must also be overcome.
The force onto a particle situated at the top of the bed is intimately related to the bottom stress
bexerted by the water flow onto the bed.Comparing the force caused by this stress (force = stress xarea), we have:
s b s s
b
gd s gd s d
) 1 ( 2 3 weight particle
force frictional ratio
) 1 6 ( 4
3 2
Then ignoring the 3/2 factor and recalling that the bottom stress
bcan be expressed in terms of the friction velocity u*, we define the dimensionless ratio:s
s s gd
u gd s Sh u
) 1 ( ) 1 (
2
* 2
*
This is called the Shields stability parameter.
The thinking then becomes a matter of comparing the actual Shields stability parameter value to a critical value for which entrainment begins.
0.047
Bed load begins when the Shields parameter Shexceeds the threshold value (gray zone) depending on the particle’s Reynolds number.
Shields stability parameter
Reynolds number
Sh
cThe Mississippi River Delta
Where the water speed slows down, suspended particles settle as sediment.
All river deltas are formed in this way.
Definitions:
- Bed = sediment particles not in motion, wet but not moving - Bed load = set of particles crawling along the bed,
dislodged by lift and drag forces but unable to stay aloft because of their weight
- Suspended load = set of particles moving with the stream - Dissolved load = concentration of chemically dissolved elements
from sediment, weightless and therefore at any level.
many collisions collisionless Bed
(dissolved chemicals)
(particles in suspension)
(particles that roll around as the water passes by) Bed
silt sand gravel
Particles switch from crawling on the bed (bed load) to being fully suspended Note: No longer Reynolds number but a measure of the particle size 2
*
( 1) s Sh u
s gd
Bedload transport
The amount of material being transported in the bedload is, per unit width of stream:
s s s s s s
s
q c u
m
crawling speed
thickness of bedload layer volumetric particle concentration (volume/volume of water) mass transported
(per unit time and unit width)
volumetric flow rate (per unit width)
8 *
. 4
) ( 5 . 2
65 . 0
u u
d Sh Sh c
s
s c s
s
A common choice is:in which case the bedload transport is found to be:
* 2
* 0.047
) 1 80 ( .
7 du
gd s
m u s s
s
s
Many other formulas have been proposed over the years
Here:
c c
s s
s
Sh Sh
gd s q m
*
*
* 3
) 1 (
Stream meandering
Excess centrifugal force of fast flow at top and insufficient centrifugal force of slow flow near bottom causes a transverse circulation, called
Secondary Circulation.
The resulting 3D flow is a helical flow.
The effect of the secondary circulation is cause a pattern of erosion at the outer bank and sedimentation at the inner bank.
(Scorer, 1997)
Sedimentation pattern in a stream meander
Evidence of erosion
Evidence of sedimentation
The state line between the states of Louisiana and Mississippi was defined as the middle of the Mississippi River at the time of the decision.
Since then, the Mississippi River has modified its course, and the border no longer coincides with the middle of the river at a number of locations, leaving pockets of Mississippi State to the West of the River, and pockets of Louisiana State to the East of the River.
Flow near the entrance of a side channel (such as an irrigation channel) will lead to unwanted sediment at the entrance of the channel eventually blocking the entrance of the side channel.
Gradual choking of entrance to side irrigation channels by sediment deposition has been claimed to have contributed to the demise of the Babylonian civilization.
Possible remedies
1. Have the entrance channel on the outside of a bend of the main channel.
2. Configure the geometry such that the flow is first partitioned and then forced to make the turn.
