1

LECTURE 5CONCEPTS FROM RIVERS THAT CAN BE APPLIED

TO TURBIDITY CURRENTS

CEE 598, GEOL 593TURBIDITY CURRENTS: MORPHODYNAMICS AND DEPOSITS

Image courtesy M. Jaeggi

Reuss River plunging into Lake Lucerne, Switzerland: flood of summer, 2005

2

GRAIN SIZE CLASSIFICATION

Type D (mm) Notes

Clay < 0.002 < -9 > 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 > 256 > 8 < -8 “

Mud = clay + silt

22D)2(n

)D(n)D(og2

3

SEDIMENT FALL VELOCITY IN STILL WATER

wheregD

vsf

RR)(f pf ReR and

andvs = fall velocityD = grain sizeR = (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

DRgDpRe

Relation of Dietrich (1982):

})](n[b)](n[b

)](n[b)(nbb{exp4

p53

p4

2p3p21f

ReRe

ReReR

b1 2.891394

b2 0.95296

b3 0.056835

b4 0.002892

b5 0.000245

The original relation also includes a correction for shape.

4

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

5

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.

6

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 ballistictrajectory 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

RcgLASF wgd

a

LA

gLAS)Rc1(F wgd

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

)tan(S a

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CRITICAL ROLE OF SUSPENDED SEDIMENT TO DRIVE TURBIDITY CURRENTS

RIVER: Suspended sediment is NOT NECESSARY to drive the flow.

RcgLASF wgd

a

LA

gLAS)Rc1(F wgd

TURBIDITY CURRENT: Suspended sediment is NECESSARY to drive the flow!

The suspended sediment in turbidity currents is composed of mud and/or sand.

)tan(S a

12

BEDLOAD TRANSPORT BY TURBIDITY CURRENTSThe same size of sand can participate in both transport mechanisms, whereas gravel is usually moved only as bedload.

Gravel/sand deposit in the River Wharfe, U.K.

Image courtesy D. Powell

Turbidity currents can transport sand, and sometimes gravel as bedload.

Gravel/sand deposit (likely) emplaced by a turbidity current, Cerro

Gordo formation, Patagonia, Chile.

13

TURBIDITY CURRENTS CAN MOVE BEDLOAD, BUT BEDLOAD DOES NOT DRIVE TURBIDITY

CURRENTS

Suspended mud and sanddrove 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.

Mud/gravel/sand deposits emplaced by a turbidity current, Cerro Gordo formation,

Patagonia, Chile.

14

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.

15

BEDLOAD AND SUSPENDED LOAD IN AN EXPERIMENTAL DELTA WITH A PLUNGING

TURBIDITY CURRENT

Kostic and Parker (2003)

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1R

X10x1c 6

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

Conversion from X to c

R 1.65X 2000 mg/literc 0.000755

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 Minnesota River Mankato

1

10

100

1000

10000

1 10 100 1000 10000

Q (m3/s)

X m

g/li

ter

SUSPENDED SEDIMENT CONCENTRATION IN A GARDEN-VARIETY RIVER

Q = flow discharge

Note: X is never higher than ~ 3000

mg/l

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SUSPENDED SEDIMENT CONCENTRATION IN A GARDEN-VARIETY RIVER contd.

Suspended Sediment Concentration Minnesota River Mankato

c = 1E-05(Q)0.388

0.000001

0.00001

0.0001

0.001

0.01

0.1

1

1 10 100 1000 10000

Q (m3/s)

c

Note: c is never higher than ~ 0.001:

highly dilute suspension

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BED GRAIN SIZE DISTRIBUTION IN A GARDEN-VARIETY RIVER

Bed Grain Size Distributions, Minnesota River at Mankato

0

10

20

30

40

50

60

70

80

90

100

0.01 0.1 1 10 100

D (mm)

Pe

rce

nt

Fin

er

GSD1

GSD2

GSD3

GSD4

GSD5

GSD6

GSD7

GSD8

GSD9

GSD10

GSD11

GSD12

GSD13

Average

Where’s the mud?

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FRACTION OF SUSPENDED LOAD THAT IS MUD IN A GARDEN-VARIETY RIVER

Percent of Suspended Load Finer than 0.062 mm:Minnesota River at Mankato

Fload<62 = [-0.0245(Q) + 87.828]/100

0

10

20

30

40

50

60

70

80

90

100

0 200 400 600 800 1000 1200

Q (m3/s)

Per

cen

t m

ud

The suspended load is mostly mud!

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IMPLICATIONS FOR TURBIDITY CURRENTS (??)

Turbidity currents are also driven by dilute (c << 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

Image courtesy J. W. Lauer

Mostly mud-free channel, Mud-rich floodplain (but with sand also)

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RIVERS AND FLOODPLAINS

Minnesota River, Minnesota

Image courtesy J. W. Lauer

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.

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SAND AND MUD

Paraná River, Argentina

Sand rich Mud rich

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APPLICATION TO LEVEED CHANNELS CREATED BY TURBIDITY CURRENTS

Bengal Fan: Schwenk, Spiess,Hubscher, Breitzke (2003)

Crati Fan off Italy, Ricci Lucchi et al. (1984); Morris and Normark

(2000)

Floodplain levee

Channel: predominantly sandy (some mud)

Levees: predominantly muddy (some sand)

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SCALE FOR GRAVITATIONAL FORCE:RIVERS AND TURBIDITY CURRENTS

flow = denote the density of the flowing amb = density of the ambient fluidU = flow velocityC = volume concentration of suspended sedimentR = (sed - f)/f = submerged specific gravity of sedimentH = depth (layer thickness) and width of control volumeWimm = immersed weight in control volume

H

H 3

ambflowimm gHW

Flowing fluid

ambient fluid

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SCALE FOR GRAVITATIONAL FORCE:RIVERS AND TURBIDITY CURRENTS

CASE OF A RIVER:flow = w(1+RC) (fresh

water with sediment)

amb = air (air)R = (sed - w)/w 1.65

H

H

CASE OF A TURBIDITY CURRENT:flow = w(1+RC) (fresh or

sea water with sediment)

amb = w (fresh or sea water)R = (sed - w)/w 1.65

3airwimm gH)RC1(W 3

wwimm gH)RC1(W

Flowing fluid

ambient fluid

H

31

x Ut

A

U

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 Ut, so that volume UtA and mass flowUtA has crossed the face in time t.

UtA

VOLUME, MASS AND MOMENTUM DISCHARGE

32

x Ut

A

U

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 AUtThe mass that crosses is flowAUtThe momentum that crosses is UflowAUt

The volume discharge Q = UAThe mass discharge Qmass = flowUAThe momentum discharge Qmom = flowU2AU

UtA

VOLUME, MASS AND MOMENTUM DISCHARGE contd.

33

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.)

Finert

Control volume

x

Force balance:

/t(x-momentum in c.v.) =

Inflow rate – outflow rate – Finert

Steady flow: no outflow of x-momentum:

inert2

flow F0AU0

AUF 2flowinert

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THE DENSIMETRIC FROUDE NUMBER:A SCALE OF THE RATIO OF INERTIAL TO GRAVITATIONAL

FORCES

H

H

Flowing fluid

ambient fluid

22flowinert HUF 3

ambflowimm gHW

H

Densimetric Froude number Frd:

gH)(

U

gH)(

HU

W

F

ambflow

2flow

3ambflow

22flow

imm

inert2d

Fr

35

THE DENSIMETRIC FROUDE NUMBER:RIVER AND TURBIDITY CURRENT

RIVER: airambwflow ,)RC1(

gH

U

gH))RC1(

U)RC1( 2

airw

2w2

d

Fr

Now for R ~ 1.65, C << 1 and air/w << 1,

TURBIDITY CURRENT:

wambwflow ,)RC1(

Now for R ~ 1.65 and C << 1,

RCgH

U

gH))RC1(

U)RC1( 2

ww

2w2

d

Fr

36

THE FROUDE NUMBERS:

gH

Ud FrFr

RCgH

Ud Fr

RIVER:

TURBIDITY CURRENT:

Most of the concepts based on Froude number for open channel (river) flow generalize to turbidity currents!

Frd < 1: subcritical (tranquil) flowFrd = 1: critical flowFrd > 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.

Sangamon River, Illinois; Fr << 1

River in Maine; Fr > 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 < 1 Supercritical: Frd > 1

Water surface

internal hydraulic jump

Image courtesy N. Strong

39

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)

40

BED SHEAR STRESS AND FLOW VELOCITY

For simplicity, approximate a river as having a wide, rectangular cross-section, so that B/H >> 1, whereB = width [L]H = depth [L]

Now denoteQw = 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

2b

f UC

41

SHEAR VELOCITY AND DIMENSIONLESS CHEZY RESISTANCE COEFFICIENT

bu

The dimensionless Chezy resistance coefficient Cz is defined as

The shear velocity u [L/T] is defined as

u

UCz

42

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]b = 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

1cos,Stansin

xB

x

gHxBS

bBx

H

43

THE DEPTH-SLOPE RELATION FOR NORMAL OPEN-CHANNEL FLOW

UHBBqQUHq www

Conservation of downstream momentum:Impelling force (downstream component of weight of water) = resistive force

xBxSgHBsinxgHB b

gHSb

Reduce to obtain depth-slope product rule for normal flow:

Conservation of water mass (= conservation of water volume as water can be treated as incompressible):

xB

x

gHxBS

bBx

H

gHSu

44

FLOW REYNOLDS NUMBER, SHIELDS NUMBERAND DIMENSIONLESS CHEZY NUMBER

45

CRITERIA FOR THE ONSET OF MOTION AND SIGNIFICANT SUSPENSION

46

THE SHIELDS DIAGRAM

47

THE DEPTH-SLOPE RELATIONSHIP FOR SHEAR STRESS IN RIVERS

48

THE CONCEPT OF BANKFULL DISCHARGE IN RIVERS

QQbf

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

49

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]= kinematic viscosity of water [L2/T]R = (s/ – 1) = sediment submerged specific gravity (~ 1.65 for natural

sediment) [1]g = gravitational acceleration [L/T2]

50

FROUDE NUMBER AT BANKFULL FLOW

51

DIMENSIONLESS CHEZY RESISTANCE COEFFICIENT AT BANKFULL FLOW

52

BANKFULL FLOW AND THE SHIELDS DIAGRAM

53

VELOCITY AND SUSPENDED SEDIMENT PROFILES IN A RIVER

54

COMPARISON BETWEEN RIVERS AND TURBIDITY CURRENTS

55

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?????