CONCEPTS FROM RIVERS THAT CAN BE APPLIED TO TURBIDITY CURRENTS

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CEE 598, GEOL 593 TURBIDITY CURRENTS
MORPHODYNAMICS AND DEPOSITS
LECTURE 5 CONCEPTS FROM RIVERS THAT CAN BE
APPLIED TO TURBIDITY CURRENTS
Reuss River plunging into Lake Lucerne,
Switzerland flood of summer, 2005
Image courtesy M. Jaeggi
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GRAIN SIZE CLASSIFICATION
Type D (mm) ? ? Notes
Clay lt 0.002 lt -9 gt 9 Usually cohesive
Silt 0.002 0.0625 -9 -4 4 9 Cohesive non-cohesive
Sand 0.0625 2 -4 1 -1 4 Non-cohesive
Gravel 2 64 1 6 -6 -1
Cobbles 64 256 6 8 -8 -6
Boulders gt 256 gt 8 lt -8
Mud clay silt
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SEDIMENT FALL VELOCITY IN STILL WATER
where
and
and vs fall velocity D grain size R (?sed -
?w)/?w submerged specific gravity of sediment
1.65 for quartz (?sed sediment density, ?w
water density g gravitational acceleration
9.81 m/s2 ? kinematic viscosity of water
1x10-6 m2/s
Relation of Dietrich (1982)
The original relation also includes a correction
for shape.
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USE OF THE WORKBOOK RTe-bookFallVel.xls
A view of the interface in RTe-bookFallVel.xls is
given below. It can be downloaded from
http//cee.uiuc.edu/people/parkerg/morphodynamics
_e-book.htm
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SOME SAMPLE CALCULATIONS OF SEDIMENT FALL
VELOCITY (Dietrich Relation)

• g 9.81 m s-2
• R 1.65 (quartz)
• 1.00x10-6 m2 s-1 (water at 20 deg Celsius)
• ? 1000 kg m-3 (water)

D, mm vs, cm/s
0.0625 0.330
0.125 1.08
0.25 3.04
0.5 7.40
1 15.5
2 28.3
The calculations to the left were performed with
RTe-bookFallVel.xls.
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MODES OF SEDIMENT TRANSPORT
Bed material load is that part of the sediment
load that exchanges with the bed (and thus
contributes to morphodynamics of the river
bed). Wash load is transported through without
exchange with the bed. In rivers, material finer
than 0.0625 mm (silt and clay) is often
approximated as wash load. Washload does
exchange with the floodplain. Washload moves in
suspension. Bed material load is further
subdivided into bedload and suspended
load. Bedload sliding, rolling or saltating in
ballistic trajectory just above bed. role of
turbulence is indirect.   Suspended load feels
direct dispersive effect of eddies. may be wafted
high into the water column.
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VIDEO CLIP ILLUSTRATING BEDLOAD IN A MODEL RIVER
IN THE LABORATORY
Wong et al. (2007)
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VIDEO CLIP ILLUSTRATING BEDLOAD AND SUSPENDED
LOAD CARRIED NEAR THE BED OF THE TRINITY RIVER,
CALIFORNIA
Clip courtesy A. Krause
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VIDEO CLIP ILLUSTRATING BEDLOAD AND SUSPENDED
LOAD CARRIED BY A TURBIDITY CURRENT
Cantelli et al. (2008)
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APPLICATION TO TURBIDITY CURRENTS
RIVER The downslope component of gravitational
force Fgd acting on the control volume to drive
the flow is
TURBIDITY CURRENT The downslope component of
gravitational force Fgd acting on the control
volume to drive the flow is
where c is the volume concentration of suspended
sediment
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CRITICAL ROLE OF SUSPENDED SEDIMENT TO DRIVE
TURBIDITY CURRENTS
RIVER Suspended sediment is NOT NECESSARY to
drive the flow.
TURBIDITY CURRENT Suspended sediment is
NECESSARY to drive the flow!
The suspended sediment in turbidity currents is
composed of mud and/or sand.
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BEDLOAD TRANSPORT BY TURBIDITY CURRENTS
The same size of sand can participate in both
transport mechanisms, whereas gravel is usually
moved only as bedload.
Turbidity currents can transport sand, and
sometimes gravel as bedload.
Gravel/sand deposit (likely) emplaced by a
turbidity current, Cerro Gordo formation,
Patagonia, Chile.
Gravel/sand deposit in the River Wharfe,
U.K. Image courtesy D. Powell
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TURBIDITY CURRENTS CAN MOVE BEDLOAD, BUT BEDLOAD
DOES NOT DRIVE TURBIDITY CURRENTS
Mud/gravel/sand deposits emplaced by a turbidity
current, Cerro Gordo formation, Patagonia, Chile.
Suspended mud and sand drove the turbidity
currents that emplaced these deposits. Some of
the currents also moved and emplaced sand and
gravel moving as bedload. (Gravel/sand deposits
can also be emplaced by submarine debris flows.)
Gravel/sand deposit emplaced by a turbidity
current, Cerro Gordo formation, Patagonia, Chile.
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THE REASON WHY BEDLOAD CANNOT DRIVE TURBIDITY
CURRENTS
Bedload moves by sliding, rolling or saltating
in ballistic trajectories just above bed.
Bedload particles are dragged by the flow.
Suspended particles drag the flow with them.
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BEDLOAD AND SUSPENDED LOAD IN AN EXPERIMENTAL
DELTA WITH A PLUNGING TURBIDITY CURRENT
Kostic and Parker (2003)
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SUSPENDED SEDIMENT CONCENTRATION
Suspended sediment concentration is often
expressed in units of mg/liter, i.e. the weight
of sediment in milligrams per liter of
sediment-water mixture, here denoted as X. The
corresponding volume concentration c i.e. the
volume of pure sediment per unit volume of
sediment-water mixture, is related to X as
Double-click to open the spreadsheet.
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A GARDEN-VARIETY SAND-BED RIVER THE MINNESOTA
RIVER NEAR MANKATO
Image courtesy P. Belmont
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SUSPENDED SEDIMENT CONCENTRATION IN A
GARDEN-VARIETY RIVER
Note X is never higher than 3000 mg/l
Q flow discharge
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SUSPENDED SEDIMENT CONCENTRATION IN A
GARDEN-VARIETY RIVER contd.
Note c is never higher than 0.001 highly
dilute suspension
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BED GRAIN SIZE DISTRIBUTION IN A GARDEN-VARIETY
RIVER
Wheres the mud?
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FRACTION OF SUSPENDED LOAD THAT IS MUD IN A
GARDEN-VARIETY RIVER
The suspended load is mostly mud!
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IMPLICATIONS FOR TURBIDITY CURRENTS (??)
Turbidity currents are also driven by dilute (c
ltlt 1) suspensions of sand and mud. Mud has a
smaller fall velocity than sand, and is thus
easier to keep in suspension. Mud is a good
driver to carry both sand (in suspension and as
bedload) and gravel into deep water.
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THE CASCADIA AND ASTORIA SUBMARINE CHANNELS OFF
THE PACIFIC COAST OF THE USA
Nelson et al., 2000
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CORES SHOW THAT THE CHANNELS MOVE MUD, SAND AND
GRAVEL TO DEEP WATER
Nelson et al., 2000
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RIVERS AND FLOODPLAINS
Strickland River, New Guinea
Mostly mud-free channel, Mud-rich floodplain
(but with sand also)
Image courtesy J. W. Lauer
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RIVERS AND FLOODPLAINS
Minnesota River, Minnesota
Sand load moves as bedload and suspended load.
Exchanges mostly with bed, but with floodplain as
well. Mud moves as suspended wash
load. Exchanges with the floodplain.
Image courtesy J. W. Lauer
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SAND AND MUD
Sand rich
Mud rich
Paraná River, Argentina
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APPLICATION TO LEVEED CHANNELS CREATED BY
TURBIDITY CURRENTS
Floodplain ? levee Channel predominantly sandy
(some mud) Levees predominantly muddy (some
sand)
Bengal Fan Schwenk, Spiess,Hubscher, Breitzke
(2003)
Crati Fan off Italy, Ricci Lucchi et al. (1984)
Morris and Normark (2000)
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SCALE FOR GRAVITATIONAL FORCE RIVERS AND
TURBIDITY CURRENTS
?flow denote the density of the flowing ?amb
density of the ambient fluid U flow
velocity C volume concentration of suspended
sediment R (?sed - ?f)/?f submerged specific
gravity of sediment H depth (layer thickness)
and width of control volume Wimm immersed
weight in control volume
ambient fluid
H
H
Flowing fluid
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SCALE FOR GRAVITATIONAL FORCE RIVERS AND
TURBIDITY CURRENTS
CASE OF A RIVER ?flow ?w(1RC) (fresh
water with sediment) ?amb ?air
(air) R (?sed - ?w)/?w ? 1.65
CASE OF A TURBIDITY CURRENT ?flow ?w(1RC)
(fresh or sea water with sediment) ?amb
?w (fresh or sea water) R (?sed - ?w)/?w ? 1.65
ambient fluid
H
H
H
Flowing fluid
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VOLUME, MASS AND MOMENTUM DISCHARGE
The tube shown below has rectangular
cross-section with area ?A. The fluid velocity
is U and the fluid density is ?flow
At time t 0 we mark a parcel of fluid, the
downstream end of which is bounded by an orange
face.
In time ?t the leading edge of the marked parcel
moves downstream a distance U?t, so that volume
U?t?A and mass ?flowU?t?A has crossed the face in
time ?t.
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VOLUME, MASS AND MOMENTUM DISCHARGE contd.
The discharge of any quantity is the rate at
which it crosses a section per unit time
The volume that crosses the section in time ?t is
?AU?t The mass that crosses is ?flow?AU?t The
momentum that crosses is U?flow?AU?t The volume
discharge Q U?A The mass discharge Qmass
?flowU?A The momentum discharge Qmom
?flowU2?AU
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MOMENTUM DISCHARGE AND INERTIAL FORCE
Aim a jet of water at a plate perpendicular to
the jet. The jet flows into the control volume in
the x direction. The jet flows out of the control
volume perpendicular to the x direction. What is
the (inertial) force Finert that the plate must
exert on the jet in order to deflect it without
moving? (Jet has cross-sectional area ?A.)
Force balance ?/?t(x-momentum in c.v.)
Inflow rate outflow rate Finert Steady
flow no outflow of x-momentum
Control volume
Finert
x
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THE DENSIMETRIC FROUDE NUMBER A SCALE OF THE
RATIO OF INERTIAL TO GRAVITATIONAL FORCES
Densimetric Froude number Frd
ambient fluid
H
H
H
Flowing fluid
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THE DENSIMETRIC FROUDE NUMBER RIVER AND
TURBIDITY CURRENT
RIVER
Now for R 1.65, C ltlt 1 and ?air/?w ltlt 1,
TURBIDITY CURRENT
Now for R 1.65 and C ltlt 1,
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THE FROUDE NUMBERS
RIVER
TURBIDITY CURRENT
Most of the concepts based on Froude number for
open channel (river) flow generalize to turbidity
currents! Frd lt 1 subcritical (tranquil)
flow Frd 1 critical flow Frd gt 1
supercritical (shooting) flow
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EXAMPLE ENTRAINMENT OF AMBIENT FLUID
In rivers, supercritical flow favors entrainment
of ambient fluid (air) into the flow, making a
diffuse interface, and subcritical flow favors
the absence of entrainment, with a sharp
interface.
River in Maine Fr gt 1
Sangamon River, Illinois Fr ltlt 1
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EXAMPLE ENTRAINMENT OF AMBIENT FLUID
In turbidity currents as well, supercritical flow
favors entrainment of ambient fluid
(sediment-free water) into the flow, making a
diffuse interface, and subcritical flow favors
the absence of entrainment, with a sharp
interface. Mixing with ambient fluid is easier
in the case of a turbidity current, because water
and air are immiscible, whereas dirty water and
clear water are miscible.
Subcritical Frd lt 1 Supercritical Frd
gt 1
Image courtesy N. Strong
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IN THE CASE OF A HIGHLY SUBCRITICAL TURBIDITY
CURRENT, THE INTERFACE CAN BE VERY SHARP INDEED
Water surface
Turbidity current interface
Toniolo et al. (2006)
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BED SHEAR STRESS AND FLOW VELOCITY
For simplicity, approximate a river as having a
wide, rectangular cross-section, so that B/H gtgt
1, where B width L H depth L Now
denote Qw flow discharge L3/T U
cross-sectionally averaged flow velocity L/T
Qw/BH ? water density M/L3 ?b bed shear
stress (force per unit bed area) ML-1T-2 Then
bed shear stress is related to flow velocity
using a dimensionless friction (resistance)
coefficient Cf, so that
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SHEAR VELOCITY AND DIMENSIONLESS CHEZY RESISTANCE
COEFFICIENT
The shear velocity u? L/T is defined as
The dimensionless Chezy resistance coefficient Cz
is defined as
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NORMAL OPEN-CHANNEL FLOW IN A WIDE CHANNEL
Normal flow is an equilibrium state defined by a
perfect balance between the downstream
gravitational impelling force and resistive bed
force. The resulting flow is constant in time
and in the downstream, or x direction.

• Parameters
• x downstream coordinate L
• H flow depth L
• U flow velocity L/T
• qw water discharge per unit width L2T-1
• B width L
• Qw qwB water discharge L3/T
• g acceleration of gravity L/T2
• bed angle 1
• tb bed boundary shear stress M/L/T2
• S tan? streamwise bed slope 1
• (cos ? ? 1 sin ? ? tan ? ? S)
• water density M/L3

The bed slope angle ? of the great majority of
alluvial rivers is sufficiently small to allow
the approximations
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THE DEPTH-SLOPE RELATION FOR NORMAL OPEN-CHANNEL
FLOW
Conservation of water mass ( conservation of
water volume as water can be treated as
incompressible)
Conservation of downstream momentum Impelling
force (downstream component of weight of water)
resistive force
Reduce to obtain depth-slope product rule for
normal flow
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FLOW REYNOLDS NUMBER, SHIELDS NUMBER AND
DIMENSIONLESS CHEZY NUMBER
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CRITERIA FOR THE ONSET OF MOTION AND SIGNIFICANT
SUSPENSION
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THE SHIELDS DIAGRAM
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THE DEPTH-SLOPE RELATIONSHIP FOR SHEAR STRESS IN
RIVERS
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THE CONCEPT OF BANKFULL DISCHARGE IN RIVERS
Let ? denote river stage (water surface
elevation) L and Q denote volume water
discharge L3/T. In the case of rivers with
floodplains, ? tends to increase rapidly with
increasing Q when all the flow is confined to the
channel, but much less rapidly when the flow
spills significantly onto the floodplain. The
rollover in the curve defines bankfull discharge
Qbf.
Minnesota River and floodplain, USA, during the
record flood of 1965
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PARAMETERS USED TO CHARACTERIZE BANKFULL CHANNEL
GEOMETRY
In addition to a bankfull discharge, a reach of
an alluvial river with a floodplain also has a
characteristic average bankfull channel width and
average bankfull channel depth. The following
parameters are used to characterize this
geometry. Definitions Qbf bankfull discharge
L3/T Bbf bankfull width L Hbf bankfull
depth L S bed slope 1 Ds50 median surface
grain size L n kinematic viscosity of water
L2/T R (rs/r 1) sediment submerged
specific gravity ( 1.65 for natural sediment)
1 g gravitational acceleration L/T2
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FROUDE NUMBER AT BANKFULL FLOW
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DIMENSIONLESS CHEZY RESISTANCE COEFFICIENT AT
BANKFULL FLOW
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BANKFULL FLOW AND THE SHIELDS DIAGRAM
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VELOCITY AND SUSPENDED SEDIMENT PROFILES IN A
RIVER
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COMPARISON BETWEEN RIVERS AND TURBIDITY CURRENTS
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REFERENCES
Under construction Dietrich, W. E., 1982,
Settling velocity of natural particles, Water
Resources Research, 18 (6), 1626-1982. Morris,
W. R. and Normark, W. R., 2000, Sedimentologic
and geometric criteria for comparing modern and
ancient turbidite elements. Proceedings, GCSSEPM
Foundation Annual 20th Research Conference,
Deep-water Reservoirs of the World, Dec. 3 6,
606- 623. Nelson, H., Goldfinger. C, Johnson, J.
E. and Dunhill, G., 2000, Variation of modern
turbidite systems along the subduction zone
margin of the Cascadia Basin and implications for
turbidite reservoir beds. Proceedings, GCSSEPM
Foundation Annual 20th Research Conference,
Deep-water Reservoirs of the World, Dec. 3 6,
714-738. Toniolo et al. (2006) Wong et al.
(2007) Cantelli et al. (2008) Schenk et al.
(2003) Ricci Lucchi et al. (1984) Kostic and
Parker (2003) Nelson????? Lamb?????