Middleton G.V. (Ed.) Encyclopedia of Sediments and Sedimentary Rocks
Подождите немного. Документ загружается.
SEDIMENT FLUXES
AND
RATES
OF
SEDIMENTATION 605
Summary
(1) Weathering is the rate-limiting step in the entire sequence
of events determining global sediment fluxes and rates of
sedimentation.
(2) Sedimentation rates vary across time, because periods of
rapid sedimentation alternate with periods of slower
deposition, quiescence, or erosion. Sedimentation rates in
various depositional environments are therefore average
values of net sedimentation.
(3) The rate of sedimentation within a basin strongly depends
on the proximity to the sediment source, such as a river
mouth or ice terminus.
(4) Very little («10 percent) of the sediment eroded from
mountains and hilltops actually makes it to the ocean.
Most of the sediment is either in flux, or being sequestered
in interior drainage basins, lakes, subsiding alluvial fans,
flood plains, coastal plains and deltaic plains.
(5) Sediment delivery via rivers accounts for approximately
95 percent ofthe global flux from land to sea. Most of that
flux is as suspended sediment load. Dissolved load and bed
load are almost an order-of-magnitude less than the
suspended load, with important regional exceptions.
(6) Drainage basin area and relief are the most important
"geological" factors in controlling the sediment load of
rivers. However, modern rivers are greatly impacted by
human activity, either through increases in soil erosion, or
through sediment load reduction from reservoir flltration.
(7) While contributing less to the modern global flux of
sediment, sediment transport by ice, wind and waves,
remains important in regions dominated by these pro-
cesses, and achieve more global signiflcance at earlier times
in the Quaternary.
James P.M. Syvitski
Bibliography
Ahnert,
F.,
1970, Functional relationships between denudation,
relief,
and uplift
in
large mid-latitude drainage basins. American Journal
of Science, 268: 243-263.
Alexander,
CR,, and
Simoneau,
A,M,, 1999,
Spatial variability
in
sedimentary processes
on the Eel
continental slope. Marine Geol-
ogy, 154: 243-254,
Andrews, J,T,,
and
Syvitski, J,P,M,, 1994, Sediment fluxes along high
latitude glaciated continental margins: Northeast Canada
and
Eastern Greenland,
In Hay, W,
(ed,), Glohal Sedimentary
Geofluxes. Washington: National Academy
of
Sciences Press,
pp,
99-115,
Clague,
J,J,, and
Evans,
S,G,,
2000,
A
review
of
catastrophic drainage
of moraine-dammed lakes
in
British Columbia, Quaternary Science
Reviews,
19:
1763-1783,
Curtis, W,F,, Culbertson,
K,, and
Chase, E,B,, 1973, Fluvial-sediment
discharge
to the
oceans from
the
conterminous United States,
US
Geological
Survey Circular, 670:
1-17,
Dedkov, A,P,,
and
Mozzherin, V,I,, 1992, Erosion
and
sediment yield
in mountain regions ofthe world.
In
Walling,
D,E,,
Davies,
T,R,,
and Hasholt,
B,
(eds,). Erosion, Debris Elows
and
Environment
in
Mountain Regions. Proceedings
of the
Chengdu Symposium, July
1992),
IAHS Publication,
209, pp,
29-36,
Douglas,
I,, 1993,
Sediment transfer
and
siltation.
In
Turner,
B,L,,
Clark,
W,C,,
Kates,
R,W,,
Richards,
J,F,,
Mathews,
J,T,, and
Meyer,
W,B,
(eds,).
The
Earth
as
Transformed
by
Human Action.
Cambridge University Press,
pp,
215-234,
Douglas,
J,, 1967, Man,
vegetation
and the
sediment yield
of
rivers.
Nature, 215: 925-928,
Fournier,
F,, 1960,
Climatet Erosion. Paris: Presses Universitaires
de
France,
Garrels,
R,M,, and
Mackenzie,
F,T,,
1971, Evolution
of
Sedimentary
Rocks. Norton,
Gilbert,
R,, 1983,
Sedimentary processes
of
Canadian arctic Ijords,
Sedimentary Geology,
36:
147-175,
Harrison,
C,G,, 1994,
Rates
of
continental erosion
and
mountain
building, Geologische Runschau, 83: 431-447,
Hay,
W,H,, 1994,
Pleistocene-Holoeene fluxes
are not the
earth's
norm.
In Hay, W,
(ed,), Global Sedimentary Geofluxes. National
Academy
of
Sciences Press,
pp,
15-27,
Hay,
W,W,, and
Southam,
J,R,, 1977,
Modulation
of
marine
sedimentation
by the
continental shelves.
In
Andersen, N,R,,
and
Malahoff,
A,
(eds,). TheFateofEossilEuelCO2 intheOcean. Plenum
Press,
pp,
569-604,
Hay,
W,W,,
Rosol,
M,J,,
Jory,
D,E,, and
Sloan,
J.L, II, 1987,
Tectonic control
of
global patterns
and
detritai
and
carbonate
sedimentation.
In
Doyle, L,J,,
and
Roberts, H,H, (eds,). Carbonate
Clastic Transitions: Developments
in
Sedimentology. Elsevier,
pp,
1-34,
Holeman,
J,N,, 1980,
Erosion rates
in the US
estimated from
the
soil
conservation services inventory,
EOS,
61:
954,
Hu,
D,,
Saito,
Y,, and
Kempe,
S,, 2001,
Sediment
and
nutrient
transport
to the
coastal zone.
In
Galloway, J,N,,
and
Melillo,
J,M,
(eds,),
Asian Change
in
the Context of Global Climate Change: Impact
of Natural and Anthropogenic Changes
in
Asia on
Global
Biogeochem-
ical Cycles. Cambridge University Press, IGBP Publication, Series
3,
pp,
245-270,
Huglien,
K,A,,
Overpeck, J,T,, Anderson, R,F,,
and
Williams,
K,M,,
1996,
The
potential
for
paleoclimate records from varved Arctic
lake sediments: Baffin Island, eastern Canadian Arctic,
In
Kemp,
A,E,S,
(ed,), Paleoclimatology
and
Paleoceanography from
Laminated Sediments. Geological Society Special Publication,
116,
pp,
57-71,
lnman,
D,L,, and
Jenkins,
S,A,, 1999,
Climate ehange
and the
episodicity
of
sediment flux
of
small California rivers, Journat of
Geology, 107: 251-270,
Jansen, J,M,,
and
Painter, R,B,, 1974, Predicting sediment yield from
climate
and
topography, Journalof Hydrology, 21: 371-380,
Kirehner,
J,W,,
Finkel,
R,C,,
Riebe,
CS,,
Granger,
D,E,,
Clayton,
J,L,, K^ing, J,G,,
and
Megahan, W,F,, 2001, Mountain erosion over
lOyr, IOk,yr,,
and
10m,yr, time scales. Geology,
29:
591-594,
Knox,
J,C, 1993,
Large increase
in
flood magnitude
in
response
to
modest changes
in
climate. Nature, 361: 430-432,
Meade,
R,H,, 1996,
River-sediment inputs
to
major deltas.
In
Milliman,
J,D,, and Haq, B,U,
(eds,), Sea-Level Rise
and
Coastal
Subsidence. Kluwer Academic Publishers,
pp,
63-85,
Miller, G,H,, Magee, J,W,,
and
Jull, A,J,T,, 1997, Low-latitude glacial
cooling
in the
Southern Hemisphere, from amino-acid racemiza-
tion
in emu
eggshells. Nature, 385: 241-244,
Milliman,
J,D,, and
Syvitski, J,P,M,,
1992,
Geomorphie/teetonic
control
of
sediment discharge
to the
ocean:
the
importance
of
small mountainous rivers, Journalof Geology, 100: 525-544,
Milliman,
J,D,,
1980, Transfer
of
river-borne particulate material
to
the oceans.
In
Martin,
J,,
Burton, J,D,,
and
Eisma,
D,
(eds,). River
Inputs to Ocean Systems. Rome, SCOR/UNEP/UNESCO Review
and Workshop, FAO,
pp, 5-12,
Milliman,
J,D,, 1993,
Production
and
accumulation
of
calcium
carbonate
in the
ocean: budget
ofa
nonsteady state. Global Bio-
chemical
Cycles,
1:
927-957,
Milliman, J,D,, Qin, Y,S,,
and
Ren, M,E,Y,, 1987, Man's influenee
on
the erosion
and
transport
of
sediment
by
Asian rivers:
the
Yellow
River (Huanghe) example. Journal of Geology, 95: 751-762,
Molnar,
P,,
2001, Climate change, flooding
in
arid environments,
and
erosion rates. Geology,
29:
1071-1074,
Mulder,
T,, and
Syvitski, J,P,M,, 1995, Turbidity currents generated
at
river mouths during exceptional discharge
to the
world oceans.
Journal of Geotogy, 103: 285-298,
Nittrouer,
CA,, 1999,
STRATAFORM: overview
of its
design
and
synthesis
of
its results. Marine Geology, 154:
3-12,
Nordin,
CF,, 1978,
Fluvial sediment transport.
In
Fairbridge,
R,W,,
and Bourgeois,
J,
(eds,). Encyclopedia of Sedimentology. Dowden,
Hutchison
&
Ross,
pp,
339-343,
Olsen,
CR,, 1978,
Sedimentation rates.
In
Fairbridge,
R,W,, and
Bourgeois,
J,
(eds,). Encyclopedia
of
Sedimentology. Dowden,
Hutchison
&
Ross,
pp,
687-692,
606
SEDIMENT TRANSPORT
BY
TIDES
Peizhen,
Z,,
Molnar,
P,, and
Downs,
W,R,, 2001,
Increased
sedimentation rates
and
grain sizes 2m,yr,
to
4m,yr,
ago due to
the influence
of
climate change
on
erosion rates. Nature, 410: 891-
897,
Pinet,
P,, and
Souriau,
M,,
1988, Continental erosion
and
large-scale
relief.
Tectonics,
7:
563-582,
Piper, D,J,W,,
1991,
Seabed geology
of the
Canadian eastern
continental
shelf.
Continental Shelf Research, 11: 1013-1035,
Powell,
R,D,, 1983,
Glacial-marine sedimentation proeesses
and
lithofaeies
of
temperate glaciers. Glacier
Bay,
Alaska,
In
Molnia,
B,F,
(ed,). Glacial-marine Sedimentation. Plenum Press,
pp, 185-
232
Prospero, J,M,, 1981, Eolian transport
to
the world ocean.
In
Emiliani,
C, (ed,), The Sea,
Volume
7,
The Oceanic Lithosphere. John Wiley
&
Sons,
801-874,
Saito,
Y,,
Ikehara,
K,,
Katayama,
H,,
Matsumoto,
E,, and
Yang,
Z,,
1994,
Course shift
and
sediment discharge changes ofthe Huanghe
recorded
in
sediments
of
the East China Sea, Chishitsu News,
476:
8-16,
Schumm,
S,A,,
1965, Quaternary paieohydrology.
In
Wright, H,E,
Jr,,
and Frey, D,G, (eds,). The Quaternary ofthe United States. Princeton
LJniversity Press,
pp,
783-794,
Smith,
S,V,,
Renwick, W,H,, Buddemeier, R,W,,
and
Crossland,
CJ,,
2001,
Budgets
of
soil erosion
and
deposition
for
sediment
and
sedimentary organic carbon across the conterminous tJnited States,
Global Biogeochemical
Cycles,
15: 697-707,
Sommerfield,
C,K,, and
Nittrouer,
CA,,
1999, Modern accumulation
rates
and a
sediment budget
for the Eel
shelf:
a
flood-dominated
depositional environment. Marine
Geology,
154:
227-241,
Stanley,
D,J,, and
Warne,
A,G,, 1994,
Worldwide initiation
of
Holocene marine deltas
by
deceleration
of
sea-level rise. Science,
265:228-231,
Summerfield, M,A,,
and
Hulton, N,J,, 1994, Natural controls
of
fluvial
denudation rates
in
major world drainage basins, Journalof
Geo-
physical Research,
99:
13871-13883,
Syvitski,
J,,
Field,
M,,
Alexander,
C,
Orange,
D,, and
Gardner,
J,,
1996c, Continental-slope sedimentation. Oceanography,
9: 163-
167,
Syvitski,
J,P,, and
Morehead,
M,D,,
1999, Estimating river-sediment
discharge
to the
ocean: applieation
to the Eel
margin, northern
California, Marine
Geology,
154: 13-28,
Syvitski, J,P,M,, 1989,
On the
deposition
of
sediment within glacier-
influenced fjords: oceanographic controls. Marine Geology,
85:
301-329,
Syvitski, J,P,M,,
1993,
Glaeimarine environments
in
Canada:
an
overview, Canadian Journat of Earth Sciences,
30:
354-371,
Syvitski, J,P,M,,
and
Shaw,
J,,
1995, Sedimentology
and
geomorphol-
ogy
of
fjords.
In
Perillo, G,M,E, (ed,), Geomorphology
and
Sedi-
mentology of Estuaries. Elsevier,
pp,
113-178,
Syvitski, J,P,M,, Lewis, C,F,M,,
and
Piper, D,J,W,, 1996a, Paleocea-
nographic information derived from acoustic surveys
of
glaciated
continental margins: examples from eastern Canada,
In
Andrews,
J,T,, Austin, W,E,N,, Bergsten,
H,, and
Jennings, A,E, (eds,). Late
Quaternary Palaeoceanography
of the
North Atlantic Margins.
Geological Society, Special Publication, 111,
pp,
51-76,
Syvitski, J,P,M,, Andrews,
J,T,, and
Dowdeswell,
J,A,,
1996b,
Sediment deposition
in an
iceberg-dominated glaeimarine environ-
ment. East Greenland: basin fill implications. Global and Planetary
Change, 12: 251-270,
Syvitski, J,P,M,, Burrell, D,C,,
and
Skei, J,M,, 1987,
Fjords:
Proeesses
and
Products.
Springer-Verlag,
Syvitski, J,P,M,, Smith, J,N,, Boudreau, B,,
and
Calabrese, E,A,, 1988,
Basin sedimentation
and the
growth
of
prograding deitas. Journal
of
Geophysical
Research, 93: 6895-6908,
Syvitski, J,P,M,,
in
press. Supply
and
flux
of
sediment along
hydrological pathways: research
for the 21st
century. Global and
Planetary Change.
Walling, D,E,, 1987, Rainfall,
runoff,
and
erosion ofthe land:
a
global
view.
In
Gregory,
K,J,
(ed,). Energetics
of
Physical Environment.
Wiley,
pp,
89-117,
Wang,
Y,, Ren,
M,-E,,
and
Syvitski, J,P,M,, 1998, Sediment transport
and terrigenous fluxes.
In
Brink, K,H,,
and
Robinson,
A,R,
(eds,).
The Sea:
Volume
10—The Global Coastal
Ocean:
Processes
and
Meth-
ods.
John Wiley
&
Sons, 253-292,
Wilson,
L,, 1973,
Variations
in
mean annual sediment yield
as a
function
of
mean annual preeipitation, American Journalof Science,
lli\ 335-349,
Woodward,
J,C,, 1995,
Patterns
of
erosion
and
suspended sediment
yield
in
Mediterranean river basins.
In
Foster, I,D,L,, Gurnell,
A,M,,
and
Webb,
B,W,
(eds,). Sediment and
Water
Quality in River
Catchments. John Wiley
&
Sons,,
pp,
365-389,
Cross-references
Climatie Control
of
Sedimentation
Compaction (Consolidation)
of
Sediments
Erosion
and
Sediment Yield
Numerical Models
and
Simulation
of
Sediment Transport
and
Deposition
Sediment Transport
by
Unidirectional Water Flows
Tectonic Controls
of
Sedimentation
Weathering, Soils
and
Paleosols
SEDIMENT TRANSPORT
BY
TIDES
Tidal currents
Tidal currents are unique among the processes responsible for
sediment transport and deposition because of their regularity,
with the speed and direction varying with thie frequency of
the governing astronomical period (see Tides and Tidal Rhyth-
mites).
tn coastal settings where the shorelines constrain
the flow, the landward- (flood) and seaward-directed (ebb)
currents typically have directions 180° apart, in a pattern that
is termed rectilinear, A period of little or no current (i,e,, slack-
water) varying in length from a few to several tens of minutes
generally accompanies each flow reversal. As a result, sediment
transport is intermittent, with episodes of sand transport (ifthe
currents are sufficiently strong) alternating with periods of
mud deposition during the slack-water intervals (Figure S6). In
open-shelf settings removed from the confining influence of
coastlines, tidal currents are rotary because of the influence of
the Coriolis force (Allen, 1997), with the direction changing
progressively through 360° over one complete tidal period. In
such situations, there is no slack-water period, although the
currents transverse to the primary flow directions generally are
slower than the main ebb and flood currents. As a result, mud
deposition is inhibited. Typically, the highest maximum speeds
are found in constricted, inshore areas, where they may be as
high as 1-2 m/s. As a result, the transport and deposition of
sediment by tides is most important in coastal zones, with tidal
currents dominating sedimentation inside the sheltered con-
fines of estuaries, lagoons, and deltaic distributary channels
where wave action is minimal (see Neritic Carbonate Deposi-
tional; Environments Deltas and Estuaries).
In the ideal case, tidal-current speeds vary sinusoidally
over an individual ebb or flood period, with equal durations
and speeds in the opposing directions. In this case, there is
no net (residual) sediment transport (Figure S6(A)), In reality,
however, various factors cause deviations from the ideal;
producing a time-velocity asymmetry that causes an inequality
in the amount of sediment transported in the two directions
(Figure S6(B)),
Tidal-wave deformation: in the shallow water ofthe coastal
zone, the crest of the tidal wave travels faster than the trough
because the latter experiences greater frictional retardation.
SEDIMENT TRANSPORT BY TIDES 607
Convergence ofthe shoreline, creating a landward decrease in
the cross-seetional area, eompounds this distortion. As a
result, the flood tide typieally has a shorter duration and
higher maximum speed than the ebb tide (Dyer. 1995).
Hypsoiiiciric
inffitenccs:
because the arca-elcvation distribu-
tion (the hyp.somctry) of coastal areas is generally not linear.
the volume of water passing through any channel will vary in
response to temporal changes in si/c ofthe area being flooded
or drained (Boon and Byrne. 1981). Thus, the maximum
eurrent speeds will tend to occur when the largest area is being
flotided or drained rather than at tnid-tide. Such hypsometric
inlluences can also cause inequalities between the maximtim
ebb and flood ctn'rents (Friedriehs attd Aubrey. 1988).
Figure S6 Tr^insport of bedload sediment by: (A) an idealized,
'.ymmf^rital Itrlal current; and (Hi a lidal current with a pronounced
lime-vetocily asymmetry. The bedload discharge Istippled area) is
approximated as: ty, /. \U,-U^,\', for
U,>U,,
(the cross-hatched
areas), wht're U, is ihe (k^plh-aver.iged lidal-current speed and (_/,r
>^
thf threshold ol bedload movement, in (A) the bedlojd discharges in
the opposite directions are equal, suth that there in no net transport. In
iBl the short-duration high speeds on one half of the tide generate
more transport than the slower, longer-duration flow in the opposile
direction,
yielding a residual Iranspori in the direclion of the faster
currents. The black rectangles at the limes of near-zero current speeds
represent tbe periods when mud can be deposited.
Residual, estuarine eireidation: at tidally influenced river
mouths, fresh water rides above denser seawater (Figure S7).
This generates a net seaward Bow in the upper layer and a
residual landward flow in the near-bed salt wedge (Nichols and
Biggs, 1985: Dyer. 1995), This so-called estuarine circulation,
which occurs in estuaries and delta distributary channels,
becomes progressively less important as the tidal range
increases, because strong tidal currents and intense turbulence
destroy the salinity stratification.
Superimposed currents: wind forcing and oceanic circulation
are responsible for slow water movement on timescales ranging
from hours to years, Sueh currents may not be suflieient by
themselves to initiate sediment movement, but may lead to
residual transport when they are superimposed on the stronger
tidal flows.
Bathymetric influenee: local bathymetric irregularities, in-
cluding bedrock promontories and current-generated sea-bed
topography (e.g., tidal bars), cause spatial variability tn the
bed shear stress, with areas faeing into the current experiencing
stronger eurrents than areas sheltered from the main flow.
Beeause of tidal flow reversals, these areas of exposure and
sheltering alternate positions on each ebb and Hood tide. This
in turn produces inequalities between the ebb and Hood
currents at most locations.
Bedload transport
The transport of sand-sized bed-load sediment by tidal
currents is generally deseribable using the concepts developed
for unidirectional flow (see .Sediment Transport hy Unidirec-
tional
Flows).
The unsteadiness assoeiated with flow aecelera-
tion and deceleration over each tidal cycle has relatively little
affect, because sand-sized sediment responses rapidly to
changes in bed shear stress (Van Rijn, 1993). Consequently.
bed-load-transport equations developed for unidirectional
flows ean be integrated over a complete tidal eyele. using the
instantaneously measured mean current speeds and water
depths, to obtain the residual bed-load discharge, provided
salinity stratification is not pronounced. Because the discharge
of bed-load is a power funetion of [he current speed, the
direetion of residual sand transport can commonly be
determined by comparing only the maximum speeds in the
ebb and flood directions, with lesser regard for the durations of
weaker currents (Figure S6(B)), Thus, the factors that
determine the residual transport of sand are those that most
strongly influenee the inequality ofthe peak speeds,
Bathymetric and hypsometric influences, coupled with any
tluvial discharge, ereate systems oiniutually evasive ehannels:
ehannels that open in a seaward direction tend to be flood
—• Residual circutation
? Suspen&on fallout
Lew
Sea
SSC
High
Figure S7 Formation of a salt wedge, as shown by the inclined salinity contours (dashed lines), in the zone of mixing between fresh water
arid seawater. The resulting, residual estuarine circulation loutward flow irt the surface layer; landward flow near the bed) traps line-grained
material and develops a zone of elevated suspended-sediment toncentrations (SSCsl called the lurbiclily m.iximum.
608
SLDIMENT TKANSP(JRT BY TIDCS
dominant, whereas channels that connect directly to a river
tend to be ebb dominant. Elongate tidal bars separate such
ehannels and have opposite direetions of net sand transport on
either side of their crest (Dalrymple and Rhodes. 1995).
Erosional hed-load partings are produced at locations where
the directions of residual transport diverge (i.e.. there are
opposing directions of net transport
1
on either side of" the
parting: Harris etal,. 1995). Conversely, net deposition occurs
in areas where the residual transport converges, Sueh a hed-
had convergence appears to be present within all estuaries
and in the mouth-bar area of tidally influenced or dominated
deltas:
sand can be moved landward from the shelf because of
the general Hood dominance caused by the shallow-water
distortion oflhe tidal wave, whereas the seaward movement of
river-supplied sediment is slowed hy the periodle eurrent
reversals. On tide-dominated eontinental shelves, bed-load
partings and eonvergences are separated by areas with a
consistent direetion of net sand transport. These seditiiem-
transportpathways may be tens to hundreds of kilometers long
and display a predictable succession of bedform^ (Belderson
et al,. 1982: see also Surface Forms).
Suspended-load transport
Compared to bed-load, the transport of suspended material is
more strongly influenced by flow unsteadiness and weak
residual currents, beeause fine-grained material eontinues to
move for some time after currents have dropped below the
threshold for bed-load movement. Thus, the transport of fine-
grained sediment may be strongly influenced by weak, residual
eurrents. and the net transport of bed-load and suspended-
load sediment may be in different, even opposing, directions.
In detail, the movement of suspended sediment lags behind
the water movement, both during deposition from a deeelerat-
ing current and during erosion by an accelerating current. Van
Straatenand Kuenen (1958; c/,'Nichols and Biggs, 1985: Dyer,
1995) developed a simplified, yet elegant, model to aeeount for
the more important affects (Figure S8). In this model, the tide
is assumed to be symmetrical and to show a linear, landward
decrease in the maximum current speed. Two lags are
considered: .settling lag—ihc distance (and time) taken for
suspended sediment to settle to the bed as the current speed
decreases toward slack water (Figure S8(A)): and .scoiirlag a
delay in resuspension from the bed because the current speed
needed to erode fine-grained seditnent is greater than the
eurrent speed at whieh deposition oeeurs (Figure S8(B)), These
two lags operate at both the landward and seaward ends ofa
sediment-particle's excursion over a half tidal cyele. However,
beeause the distance-velocity distributions are asymmetrieal
(even though speeds at any point are sinusoidal), the lags
are longer at the landward end. Furthermore, the water
and particle excursion distances decrease toward the land (i.e.,
E-E' is shorter than F F': Figure S8), Thus, there is a net
landward migration ofthe partiele and a resulting tendency for
fine-grained sediment to aeeumulate near the landward margin
of tidal flats and at the head of estuaries.
The foregoing illustrates that the transport and deposition of
fine-grained sediment is strongly influenced by the faetors
governing the erosion threshold. Unlike noncohesive satid for
which the threshold-of-motion is essentially constant for a give
grain size, the erosion threshold for mud is not constant and
inereases as the degree of consolidation increases (Parchure and
Mehtii, 1986), Thus, the longer slack-water period that
(A) Settling lag only
F 1 E'7
Distance offshore
4 F' E
Und
(B) Settling
/
/
+ scour lag
6
.^ Landward migration of particle
after
one
tidal cycle
"^x~~~--^,^
Erosion Ihreshold
3^, ^^s. DeposTtioo threshold
E'7
Distance offshore
4 F'
Land
Figure S8 Transport history of suspended sedimenl in <i tidal
environment, based on Van Straaten and Kuenen (19,5!!), in a situation
where ihe maximum curreni speeds decrease toward the Itind (dashed
diagonal line in (Ai and IB)I. The presence of a single upper bound for
both ihe flood and ebb current speeds implies ihat Ihe waier
movement is symmeirical, wifh no net water distharge. In (A) only the
effect of settling lag is examined. Water originating^ al
poin!
F
on the
tlood tide enlrains .i particle al locralion
1
when the speed exceeds tbe
ihreshtild velocity
(21,
The particle then travels landward wilh the
current, eventually beinj; deposited at 4, which is located some
distance landward of point i where ihe current speed lalls helow the
ihreshold for continued movement. The distance utnd corresponding
lime inlerval) between ^ and 4 is termed ihe settling l,ig. On the
ensuing ebb tide, water originating at F' retraces the F-F' trajectory, but
is nol able to re-entrain the particle because the speed has not reached
the threshold hy the time Ihe water reaches location 4, Instead, water
origin.iting at
F
re-entrains the particle, carries it seaward along the
trajectory F-E', and deposits il at 7, The distance ol travel between 6
and 7 is also a result of the settling lag. However, because of the
distance-velocity asymmetry and ihe shorter excursion on the ebl) tide,
the particle experiences
a
net landward dis[)lacement
{^
->7). Note that
a particle coming to rest landward of point X in (A) cannot be re-
entrained by the tidal currenis shown because the maximum current
speed is olwtiys below the threshold. (Bi shows a similar transport
history but introduces separate erosiun and deposition thresholds,
which is more realislic than the situation shown in (A). As a result of
the higher erosion threshold, poini
E
is located further landward than
in IAI. This causes an increased dc^lay in the fe-entrainment of the
particle whic:h Van Straaten and Kuenen (1958) termed the scour Lig.
(Note that the definition of stour lag given by Nichols and Biggs (1985)
and Dyer (1995) is not precisely the same as the original definitionl.
Because of the scour lag, tbe particle does nol travel as far seaward and
experiences a greater, net landward displacement than in (A). (A) and
(B) after Figures S7 and 4, respectively, of Van Siraaten and Kuenen
(19581.
characterizes more landward locations promotes higher erosion
thresholds, longer seour lags, and prefc'rential mud deposition.
Exposure to ihe atmosphere, especially at times of high
evaporation potential, and the growth of microbial coatings
are particularly effective at produeing cohesion (see Tidal
Flats),
The residual estuarine circulation discussed above is also
significant with regard to the trapping of suspended sediment
in coastal settings. The suspended sediment introduced by the
river moves seaward in the surficial layer, but then settles into
the landward-moving lower layer (Figure S7). a process that is
SEDIMENT TRANSPORT BY UN1DIRF(T1ONAL WATER ELOWS 609
by (he flocculation o'i line-grained sediment thai occurs
in thi.s region (Nichols and Biggs, 1985: Burban
etaf.
1989:
Dyer. 1995). This circulation leads to the increase of
suspended-sediment concentrations (SSCs) near the limit of
salt-water intrusion (Nichols and Biggs. 1985: Dyer. 1995),
The higher transport capacity that characterizes the flood tide
in many eases, beeause of the shallow-water deformation o\'
the tidal uave (see above), also contributes to the trapping ol'
line-grained sediment near the landward limit oC tidal
influence. The combined influence of these factors produces a
ttirhiditytna.ximuni in which SSCs are elevated relative to areas
further landward or seaward (Figure S7), SSCs in the turbidity
maximum tend to increase as the tidal energy increases, and
thus tend to be highest in maerotidal areas and at spring tides,
because of greater restispension ot" mud. Near-bed SSCs ean
exceed lOgl ' producing mobile sediment bodies that are
called fluid mud {Vans, 1991). These dense suspensions occupy
ehaiincl-bottom locations where they can form anomalously
thick mud deposits. The high SSCs promote this deposition b\
decreasing the bed shear stress (Li and Gust. 2000) during the
ensuing tidal current. As a result, higher mean eurrent speeds
are needed to resuspend the sediment than would be the ease in
the absence of the high SSCs.
Summary
The transport of sediment by tidal currents is complex because
ol' the pronouneed temporal and spatial variability of flow
strength and direction. Sediment particles of ditTerent sizes
respond to the flow unsteadiness with different amounts of lag,
sueh that bed-load and suspended load can display different
directions of residual transport: bed-load tends to move in the
direetion o\' the current with the higher peak speed, whereas
the suspended load commonly moves in the direction of the
residual water movement. Bathymetric and hypsometric
influences produce spatial inequalities in the strengths of the
flood and ebb currents, creating complex transport pathway^.
characterized in coastal areas by mutually evasive channels.
The common development of a flood dominance because
of the distortion of the tidal wave in shallow water, coupled
with the presence of a density-driven estuarine circulation,
leads to the trapping of both bed-load and suspended-load
material within estuaries and/or at the mouth of deltaic
distributaries. Fluid mud is commonly formed beneath the
turbidity maximum ihat forms as a result of this trapping.
Robert W. Dalrymple and Kyuiigsik Choi
Bibliography
AlL-n. I',A,. IW7, Eurih Sitrlmc
Processes.
Blackwell Scienec,
IkldLTsoii. R,H,. Johnson. M.A,. and Kciiyon. N.H., 1982. Bedlorms.
hi Stride. A,H, (cd,).
Offshore'Eidal
Saiuls:
Proeesses
and Deposits.
New York: Chapman and Hall, pp, 27 .^7,
Boon, J.D,. and Byrne, R.J., lysi. On basin hypsoniotry and ihc
morphodynamic response oTcoiistal iiiloi syslems, Murinc Geologv.
40:
27 48.
Biirban.
P,-Y.,
Lick, W,, and Lick. J,. 1^89, The lloccLilalion of fine-
iirained sedimcnls in estuarine wiuers. Journal of Geophvsieul
''Research.
94: 832.1 83.10.
Dalrymple. R,W,. and Rliodes. R.N,. 1995, Lstuarinc dunes and
bartorms. In Perillo. G,M,E. (ed,|. GeomorphologyunilSedimenlol-
ogv of Esiiiarii's. Elsevier. Developments in Sedimentology 53,
pp,
359-422-
Dyer. K.R.. 1995, Sediment iranspori processes in eslu^ries. In Perillo.
G.M.E. (ed,). Geomorphology and Sedimentology «l EsUiavifs.
Amsterdam: Elsevier. Developments in Sedimentology 53, pp.
423-449,
Eaas.
R.W., 1991. Rhcological boundaries ol' mud: vvlieii,' are ihe
limils,'
Geo-Mariiie Eeilcrs. II: 143-146,
Friedriehs, G,T., and Aubrey. D,G,. 19XK, Non-linear tidal disloriion
in shallow well mixed estiiaries: a synihesis, Estuarine. Coastal and
Shelf Science. 27: 521 546.
Harris, PT.. Pattiaratehi. C.B,, Collins. M.B,. and Dalrymple, R,W,,
1995.
Whai is a bedload parling,' In Flemming. B.W,, and
Barloloma, A, (eds,), Tidal Signuttnes in Modern itnd
.Aneicni
Sedi-
menis. Inlcrnalional Association ol' Sedimentologists. Special
Publication. 24. pp. 2 10,
Li,
M.Z,. and Gust. G,, 2000, Boundary layer dynamics and drag
rcduelion in Hows of high eohesive sediment suspensions. Sedi-
menlologv. 47: 71 86,
Nicho)s.M.M,,andBi{;{;s.R,B.. 1985, Esiuarie.s, In Davis. R.A. Jr. (ed.).
CoastalScdimcniaiyEnvironments. Springer-Verlag. pp. 77-186.
Parehuie. T.M,, and Mehla. A.J,, 19S6, Erosion of soft cohesive sedi-
ment deposits. Journal<>f Hydraulic Engineering. llL 1308 1326,
Van Rijn, L.C, 1993. Principles of Sediment Iransptirt in River.s. Estu-
aries, and
CoastuI
Scus. Amsterdam: Aqua Publications.
Van Straaten. L.M,J,U,. and Kuenen. Ph.H,. 1958, Tidal action us a
cause of elay accumulation. Joiirnulof Sedimeiiturv Peirology. 28:
406 413,
Cross-references
Deltas and Estuaries
Floceulation
Nerilie Carbonate Deposilional Environments
Surface Forms
Tidal Flals
Tides and Tidal Rhvthmiles
SEDIMENT TRANSPORT BY UNIDIRECTIONAL
WATER ELOWS
Sediment properties
Description of sediment movement involves terms sueh as
grain size, shape and density, settling velocity, and sediment
transport rate. F^or the range of grain size, shape and density of
sediment available lor transport see Grain Size and Shape.
Methods of measuring and analyzing these grain properties are
described also in Carver (1971) and McManus (198S). A
sediment grain immersed in water experiences a hydrostatic
pressure that is greater on its base than on its top: an upward
directed buoyancy force equal to the weight of water displaeed
by the grain. If the weight of the grain exceeds the buoyancy
foree, the grain will sink. The immersed
weight
of the grain is
the gravity force minus the buoyancy foree, given by
Vg ((7-p), where V is grain volume, ,^' is gravitational
acceleration, a is sediment density, and p is fluid density.
Drag on sediment grains
A fluid moving relative to a solid boundary, sueh as water
flowing over a bed of sediment or a sedimenl grain settling in
water, experiences resistance to motion due to the action of
various types of frietional forees (e.g., viscous shear siress,
dynamic pressure). This resistanee to motion is called drai^.
Drag due to viscous shear is called surface drag or skin-frietion
drag, whereas drag due to fluid pressure is ealled form drag. In
turbulent (lows, form drag is normally much more important
than surface drag.
610 SEiDIMFNT TRANSPORT BY UNIDIRECTIONAL WATER FLOWS
A general equation for the drag force is: linear function of drag. As
(Eq. I)
where C), is n drag coefficient, a is the cross-sectional area
exposed to the drag, and
V,.
is the relative velocity of the solid
and fluid. The term in braekets is actually the dynamie pres,sure
on the area of the solid that faces the fluid tlow, but this term
also accounts for the pressures on the lee-side of the solid
associated with flow separation, and for viscous forees. Flow
separation produces a pressure against the flow (form drag).
The drag eocfflcicnt takes into account whether or not flow
separation occurs behind a solid body, and the nature of such
flow separation, ineltiding the size ofthe separation eddies. The
drag coefficient therelbre depends on the geotnetry ofthe solid
body, and speeifieally how streamlined it is. The drag coefficient
is also dependent on an appropriate Reynolds number, as this
determines the relative importiince of viscous drag and form
drag. The drag equation is used in two important eases: (1) the
settling of grains in fluids (See Grain
Threshold.
Grain Settling):
and. (2) fluid moving over beds of sediment.
Drag and lift on bed grains
The mean drag force acting on bed grains is commonly
resolved into components parallel to the bed (drag) and
normal to the bed (lift). The mean drag on a sediment grain
can be expressed as:
= Cp
a(pu-/2)
(Eq, 2)
where u is the mean velocity ofthe fluid at the level of effeetive
mean drag. This velocity is proportional to the square root of
the bed shear stress, z,,. The level of effective drag depends on
the shape of the grain and its position in the bed. The drag
coefficient for single grains resting on the bed is similar to that
for settling grains. The area exposed to drag depends on the
shape ofthe grain, and how it is packed in the sediment bed.
This area will be proportional to the square of grain size. Thus,
it ean be shown that
FflXT.D- (Eq.3)
where the constant of proportionality depends on the grain
shape and orientation, its relative protrusion above the mean
bed level, and the grain Reynolds number.
Both turbulent and nonturbulent fluid lift forces can act on
bed grains (summary in Bridge and Dominic. 1984). Non-
turbulent lift forees are pressures caused by asymmetrical ilow
around near-bed grains. As turbulenee originates very elose to
the bed of a stream, bed grains are undoubtedly alTected by
turbulent lift, and this is most likely to be dominant over non-
turbulent lift (outside the viseous sublayer). Fluid lift is
commonly expressed in a similar way to drag, but using a lift
coefficient instead ofa drag coefficient.
The threshold of transport of cohesionless sediment
(sand and gravel)
If fluid drag and lift forces exceed the forces keeping sediment
grains in place on the bed (gravity and cohesive forces
associated with vegetation, microbial coatings, eementation,
and clay minerals), the grains will be entrained by the flow. In
the case of cohesionless grains, the threshold of entrainmenf
depends on the balance between the drag and gravity forces.
Fii and Fl, respectively, as long as fluid lift is assumed to be a
and
Fu
x(a-
the threshold of entrainment should depend on
(Eq. 4)
fEq. 5)
(Eq. 6)
where 0 is referred to as the dimensionless hed
,shear
stress
(a measure of sediment mobility) and D is a grain size
representative of all grains in the bed. Values of dimensionless
bed shear stress at the threshold of motion are typieally
between 0,03 and 0,06 (Figure S9: based on numerous
theoretical and experimental studies, reviewed in Miller efal,.
1977;
Yalin and Karahan, 1979; Wiberg and Smith. 1987:
Bridge and Bennett, 1992: Komar, 1996: Buttington and
Montgomery. 1997). The exact value of 0 depends on the
degree to which the grains are immersed in the viscous
sublayer, the relative magnitude ofthe lift eomponent of drag.
the bed slope, and the relative size, shape and arrangement of
the grains in the bed.
The boundary grain Reynolds number (Figure S9) is
defined as
Re,, = U*
where (/* = ^
viscosity, and
10
1
01
0,001
(Eq. 7)
TJP)
is the shear velocity, v is kinematic
is the thickness of the viscous sublaver. Thus,
Suspmded loEd
10-
(Pa)
Suspended IcaJ
No movement
0,001 0,1
10
100
Figure S9 Threshold of motion (shaded zonesi for bed load .ind
suspended load for the case of cohesionless sediment. Bawd on
numerous experimental dnd [heorelicdl studies discussed in text.
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
SEDIMFNT TRANSI'ORT BY UNIDIRECTIONAI WATFR MOWS
and eaeh other. These grains form the bedload. The continuing
movement of bed-load grains requires the existence of an
upward dispersive force (Bagnold. 1966. 1973) that must be
exactly balanced by the immersed weight ofthe moving grains
for steady bed-load transport. The two ways of dispersing
grains normal to the flow boundary are by collisions between
the grains and bed. and by fluid lift.
Saltation is the dominant mode of bed-load transport, with
rolling and sliding only occurring near the threshold of
entrainment and between individual jumps (summary in
Bridge and Dominie, 1984). As the downstream veloeity of
rolling and sliding grains inereases over an irregular bed. the
grains are frequently launehed upward as they are forced over
protruding immobile grains, thus initiating saltations. At low
transport rates, saltation trajectories arc unlikely to be
interrupted by collisions with other moving grains. However,
at higher sediment transport rates (greater concentration of
bed-load grains), saltations will be more interrupted by
collisions between moving grains, and these collisions will
contribute to the upward dispersive stress.
Both turbulent and non-turbulent fluid lift forces can act on
bed-load grains (sumtiiary in Bridge and Dominic. 1984). Non-
turbulent lift forces are pressures arising from a net relative
velocity between grains and surrounding fluid. They are caused
by asymmetrical flow around near-bed grains, the redticed
grain velocity relative to the velocity gradient in the surround-
ing fluid (shear drift), and the cfTeets of grain rotation (Magnus
lift).
It is very diffieult to specify their individual contribution to
net lift, particularly when complex grain collisions occur within
the bed load, and when turbulent lift fbrccs are dominant.
As turbulence originates very close to the bed of a stream,
bed-load grains are undoubtedly affected by turbulent lift as
well as by drag. As near-bed turbulent fluctuations increase
with bed shear stress (or shear velocity), grain saltations are
modified more and more by turbulence as bed shear stress and
sediment transport rate increase. Turbulence affects differenl
sized grains in different ways, depending on immersed weight
of grains and the direction and magnitude of ttirbulent fluid
motions (review by Bridge, 2003),
The mean height ofthe bed-load (saltation) zone eontrols the
effective roughness ofthe bed. and must be known to calculate
bed-load transport rate. Many approaches to determining the
mean height of the bed-load zone are theoretical-empirical,
predicting that saltation height increases with sediment size and
some measure of sediment transport rate (reviews by Bridge
and Dominie. I9H4; Bridge and Bennett, 1992; Bridge. 2003). In
general, saltation height is proportional to grain diameter.
Theoretical models of saltation trajeetories of individual grains
have also been used to determine saltation height. However, it
is very difficult to model the influenee on saltating grains of
turbulent fluid motions, and the effects on grain trajectories of
impacts among grains are not considered.
Suspended load
Grains of clay, silt and very fine sand generally travel within
the flow, supported by upward-directed fluid turbulence. The.se
grains, the suspended
load,
travel at approximately the same
speed as the surrounding fluid beeause they are not decelerated
by intermittent eollisions with the bed. Maintenance of a
suspended-sediment load requires the existence of a net
upward-directed (luid stress to balanee the immersed weight
of the suspended grains. This can only arise if Ihe vertical
component of turbulence is anisotropie (Bagnold. 1966), This
anisotropy can be associated with the turbulent bursting
phenomenon, whereby sediment is suspended mainly in
vigorous upward ejections of fluid, and then returns to the
bed under the influence of gravity and downward-directed
turbulent motions. This idea is supported by experimental
observations of discrete clouds of suspended sediment
associated with turbulent ejeetions, and the wavy trajectories
of suspended grains (review in Bridge, 2003). However,
sediment is also suspended in vortices generated by eddy
shedding lYom the separated boundary layer in the trough
regions of ripples and dunes. With dunes, these vortiees can
reach the water surface as boils or kolks. Provided that a grain
experiences more upward directed turbulent motions than the
combination of downward directed turbulent motions and
gravitational settling, it will remain in suspension.
Two criteria for the suspension of sediment are:
rms v+ > f^^ (Eq. 8)
rms v'l - ;7);.vv' > V^ (Eq. 9)
where rms v' is the root mean square of the vertical turbulent
fluctuations ofthe flow, the subscripts refer to upward motions
(
+
)
or downward motions (-), and
V^.
is the mean terminal
settling veloeity of the sediment. The first criterion indieates
that, as long as time-averaged upward-dirceted turbuleni
velocities are in excess of l'\,. sediment ean be moved upward
within the flow, even ifthe sediment eventually returns to the
bed. The second eriterion indicates that for a grain to remain
in suspension the time-averaged upward-direeted turbulent
velocity experienced by the grain must exeeed the downward-
direeted veloeity plus the settling velocity ofthe grain. There is
an empirical relationship between the time-averaged upward
and downward directed velocities and the overall rms v' near
the bed. sueh that the two suspension criteria above beeome
armsy >
where (/ is 1,2 to 1,5
hrmsv' > l'^ where h is 0.4 to 0,9
(Eq. 10)
(Eq, 11)
Furthermore.
rmsv'IU*
^ I near the bed. so that ihe suspension
criteria for near-bed conditions are
aU* >
V^.
and hU* > V^
(Eq, 12)
Also,
as the shear veloeity aud the settling velocity can be
related to the dimensionless bed shear stress and the grain
Reynolds number, the threshold of suspension can be
represented on the threshold of enlrainment diagrams
(Figure S9). As the bed shear stress varies in time and space,
sediment with a particular settling veloeity (or grain size)
may travel as both bed load and sediment load. This is
particularly true ofthe sand sizes coarser than about O.I mm.
This is called intermittentlysiispeiulcdload.
The i\'ashh)adis eommonly distinguished from suspendedhcd-
materialload. Wash load is very finegrained and suspended even
at low flow velocity. Furthermore, the volume eoneentration of
wash load does not vary much with distance from the bed.
whereas the volume concentration of suspended bed-material
load decreases markedly with distance from the bed. Whereas the
suspended bed-material load originates from the bed. the wash
load can come from bank erosion and overland flow. Perhaps, the
iwo different suspension criteria effectively distinguish wash load
from suspended bed-material load.
SFDIMENT TkANSK)KT BY UNIDIRECTIONAl WATER FLOWS
61 ;
Effect of sediment transport on flow characteristics
In uniform, uirbulent boundary layers over planar beds with
sedimenl transport, it is generally recognized that the moving
sediment modifies flow charaeteristies. Many seientists in the
1940s to 1960s (reviewed in ASCE. 1975) suggested that the
presenee of sediment in the flow caused a reduction in
turbulent eddy sizes and in the degree of turbulent mixing.
The main effeei of sediment on turbulence was expeeted to be
near the bed where sediment coneentration is highest. These
conclusions have been substantially eonfirmed by reeent
studies (review by Bridge. 2003). The nature ofthe interaction
between sediment grains and Iluid ttirbulenee aetually depends
on the relative veloeity of the grains and the turbulent fluid
(which depends on grain weight), and the relative size of the
grains and the turbulent eddies. Ifthe relative velocity ofthe
grains ;md iluid is large (i.e.. large, heavy grains), turbulence
intensily (partieularly ofthe smallest eddies) is increased as a
result of vortex shedding or inertial effects. If the relative
velocity is small (i,e., small grains), turbulence intensity is
decreased as the turbulent energy is transferred to the grains.
More reeently it has been suggested that turbulent mixing is
suppressed because ofthe density stratification hrought about
by an upward deerease in suspended sediment concentration,
as represented by a flux Richardson mimhcv. However, this idea
is not well supported by natural data (Bennett daf. 1998). In
natural Hows, bed forms have an overwhelming effect on
turbulence intensities and eddy sizes.
Sediment transport rate (bed load)
The sediment
tran.sport
rate is the amount (weight, mass, or
volume) of sediment that can be moved past a given width of
flow in a given time. The sediment transport rate controls the
development of bed forms such as ripples and dunes, the
nature of
crav/V)/;
and deposition, and the dispersal of physically
transported pollutants. There is a vast and eomplicated
literature on the subject (reviews in
Graf.
1971; ASCFi, 1975;
Yalin. 1977; Van Rijn. 1984a,b,c: Chang. 1988: and many
others) and only the basies will be presented here.
Bed-load transport rate can be expressed as
/. =
WuH
(Eq, 13)
where //, is the bed-load transport rate as immersed weight
passed per unit width, H'is the immersed weight of bed-load
grains over unit bed area, and ti,, is the mean bed-load grain
veliK'ity. The contacts beiween bed-load grains and the bed
result in resistance to forward motion. Therefore, the fluid
must exert a mean downstream force on the grains to maintain
their steady motion. For bed-load transport on a bed of slope
angle fi. the force balance parallel to the bed can he expressed
T,, + M^'sin fi = T
(Eq, 14)
where r,, is ihe bed shear stress applied to the moving grains
and immobile bed (but excluding form dtag due to bed forms
and banks), IVsin fi is the down-slope weight component of
the tiioving grains per unif bed area (with sin/J positive ifthe
bed slopes down flow), T is the shear resistance due lo the
moving bed load, and T, is the residual shear stress carried by
the immobile bed. Bed-load shear resistance can be expressed
where /•'/ is the net lltiid lifl on bed-load grains per unit bed
area, taken as resulting dominantly from anisotropie turbu-
lenee. and given by
Fl =
W{hU*/V^f
(Eq. 16)
and tan y is the dynamic friction coefficient, l-rom experiments
on shearing of grains in dry grain (lows and eoaxial drums,
where volumetric grain eoneentralions are approximately 0.5,
tan
X
eommoniy lies between 0,4 and 0,75 (review in Bridge
and Dominic. 1984; Bridge and Bennett. 1992). The residual
fluid stress r,, equals the bed shear stress at the ihreshold of
motion r,. according to Bagnold (1956. 1966). Thus, once the
applied fluid stress exceeds the value neeessary for entrain-
ment, grains will be entrained until the bed-load resistance
caused hy their motion reduces the applied fluid stress to the
threshold value of r,,. Therefore, the immersed weight of grains
moving per unit bed area is given, from equations 14 to 16, as
r,,
—
r,
tan
X
cos
fi
-
-sin/f
(Eq. 17)
As the threshold of suspension is reaehed. the term in square
brackets approaehes zero, indicating that the weight of bed-
load grains approaches infinity. In reality, this situation eould
not arise because high grain concentrations in the bed load
layer would occlude fhe bed from fluid drag and lift, thus
limiting the weight of bed-load grains (e.g., Bagnoid. 1966),
Furthermore, high concentrations of near-bed grains modify
turbulenee characteristics above the bed. In many natural
flows, the bed-slope is small enough such that sin/f tends to
zero,
and the term in square brackets tends to I. so that
(Eq. 18)
tana
The mean velocity of ihe average bed-load grain is given by
Uh
=
Un
-iiK (Eq. 19)
where ti/, is the time-averaged Row velocity at the level of
effeetive drag on the grain, and i/« is the relative velocity ofthe
fluid and the grain. The relative velocity is that at which the
fluid drag plus down-slope weight component on the grain is in
equilibrium with the bed-load shear resistanee:
Fn -^
/"V,
sin/i
—
F(,
tan x(cos/( - (hiU/ Vg)') (Eq, 20)
Using the general drag equation for Fp. and the fact that F^ is
equal to the fluid drag at a grain's terminal settling velocity,
results in
"« = KL.(tana(cosp - (nO'*/!^^)") - sin/i) " (Eq.21)
Finally, as ui)fU*=a. the mean velocity of hed-load grains is
given by
(Eq.22)
(Eq, 23}
Furthertnore. as the grain velocity must be zero at the
threshold of grain rnotion, this equation may also be written as
or approximately as
J,/, = aV* -
-
(H'cos/f-
(Eq. 15)
x/tan
y.,
(Eq.24)
614
SEDIMENT TRANSPORT HY UNIDIRFCTIONAL WATER ELOWS
Determination of the value of a requires knowledge of the
height above the bed levet ofthe effective drag on the grains
(that varies with the saltation height) and details of the
near-bed velocity profile. There have heen numerous attempts
to relate saltation height to some measure of flow stage (review
in Bridge and Bennett. 1992). The flow velocity at the height of
effective drag depends on whether the flow is hydraulically
smooth, transitional or rough. For transitional and rough
flows, a is ahout 8-12 (Bridge and Dominic. 1984). Also, at the
threshold of suspension, the grain velocity approximately
equals the fluid velocity and
Uh
= aU'. which is another
suspension criterion.
Thus,
the final approximate hed-load transport equation
can he written as
a
tan 1
(Eq, 25)
Equations of this form have heen developed, using similar
principles, hy a number of workers (details in Bridge and
Dominic, 1984), This equation agrees very well with experi-
mental dafa for flows over plane heds. For low sediment
transport rates (lower-stage plane beds), alXany. is approxi-
mately 10. but is approximately 17 for high sediment transport
rates (upper-stage plane beds). For beds covered with bed
forins such as ripples and dunes, the bed-load transport
equation can be applied by determining the average bed shear
stress over a number of bed forms, and to remove the part of
the total average stress that is due to form drag in the lee ofthe
bed forms, because it is ineffective in moving bed-load grains
(e.g., Engelund and Hansen. 1972: Engelund and Fredsoe,
1982;
Nelson and Smith. 1989), However, bed-load transport
rates associated with ripples and dunes can also be calculated
from knowledge of their mean height and downstream
migration rate.
The bed-load transport theory developed above is for mean
flow and sediment characteristics, but it can he adapted for use
with heterogeneous sediment and with temporal variations in
bed shear stress (e.g.. Bridge and Bennett. 1992), In this case, it
is necessary to specify the proportion of the different grain
fraetions available in the bed for transport, and the thresholds
of entrainment and suspension for eaeh ofthe grain fractions.
It is also necessary to speeify the proportion of time that a
particular bed shear stress acts upon the hed-load. requiring a
frequency distribution of hed shear stress. Bridge and
Bennett's (1992) bed-load transport model for heterogeneous
sediment agrees well with natural data. Models such as this
(e.g., Wiberg and Smith, 1989; Parker, 1990) are essential for
quantitative understanding of sediment sorting during erosion,
transport and deposition.
Sediment transport rate (suspended load)
Suspended-sediment transport rate at a point in the flow is
commonly expressed as
/, =u.C (Eq, 26)
where »,. is the average speed ofthe sediment (approximately
the same as the fluid velocity), and C is the volume
concentration of suspended sediment. The units of /\ are
therefore volume of sediment transported per unit cross-
sectional area normal to the tlow direetion per unit time. The
vertical variation of the velocity of suspended sediment and
fluid can be calculated using an appropriate velocity profile
law (e.g.. the law of the wall). Calculation of the vertical
variation of C in steady, uniform water Hows is traditionally
based on the balance of downward settling of grains and fheir
upward diffusion in turbulent eddies, i.e.,
V^C + i:,iiC/dy =
O
(Eq, 27)
where the first term is the rate of settling ofa particular volume
of grains per unit volume of fluid, the second term is rate of
turbulent difTusion of sediment per unit volume, and (, is the
diffusivity of suspended sedimenl (equivalent to a kinematic
eddy viscosity. 0- This balance ean also be written for
individual grain fractions. In order to determine C at any
height above the bed, v. it is necessary to calculate the vertical
variation in (,. Assuming that
(„.
= fii, where/i is close to 1, and
that the law of the wall extends throughout the flow depth,
results in the well-known Rouseci/uation
C_
d-y
(I-a
(Eq.
28}
where C,, is the value of Cat i' = (/. This equation predicts that
C decreases continuously and smoothly with distance from the
bed. as would be expected in view of the fad that turbulenee
intensity also decreases with disfanee from the bed. The
distribution of suspended sediment beeomes more uniform
throughout the flow depth as exponent r decreases, fhat is as
settling velocity (grain size) decreases and/or as shear velocity
(near-bed turbulence intensity) increases (Figure SlO). For
example, a decrease in water temperature causes an increase in
fluid viscosity, which may in turn cause a deerease in settling
velocity and an increase in suspended sediment coneentration.
The Rouse equation has been shown to agree with measured
suspended-sediment concentrations in the lower part of stream
flows but eoneentrations tend to be overestimated in the upper
parts (figure S2). This discrepancy is addressed helow.
Some of the assumptions used in developing the Rouse
equation have heen criticized: mainly the choice of velocity
proflle (law of the wall), and the fact that the interaetion
between suspended sediment, fluid properties and turbulence is
not considered. Perhaps the most serious concern with the
Rouse equation is that the sediment diffusivity has rarely been
calculated directly using quantitative observations of the
motion of sediment in turbulent eddies. Thus, there is doubt
about the vertical variation of <^ and /J (e.g.. ASCE. 1975;
Coleman, 1970; Van Rijn. 1984b). Bennett etal. (1998) have
measured turbulent motions of suspended sediment and
concluded that fi is indeed close to 1. However, suspended
sediment concentration in the upper half of the flow depth in
natural flows is eommonly larger than predicted by the Rouse
equation. One reason for this discrepancy eould be that
sediment grains that are suspended to the higher levels in the
flow are not associated with mean turbulence characteristics as
specified in fhe Rouse equation, but with turbulent eddies with
the greatest turbulenee intensities and mixing lengths (Bennett
ei af. 1998). Thus, the Rouse equation, based on average
turbulenee characteristics, may only be strictly applicable for
the lower parts of the flow.
Application of the Rouse equation in praetiee requires
ealeulation of C',, and a. and there are various methods for
doing this (review by Bridge, 2003), Nornialfy. C^ is calculated
at a position within or at the top of the hed-load layer. If bed
waves are present, a can he taken as half bed-wave height or
equivalent roughness height (Van Rijn, 1984c). The mean
volume concentration of grains in the bed-load layer, C,,. is the