Transcript Slide 1

CEE 598, GEOL 593
TURBIDITY CURRENTS: MORPHODYNAMICS AND DEPOSITS
LECTURE 5
CONCEPTS FROM RIVERS THAT CAN BE APPLIED
TO TURBIDITY CURRENTS
Image courtesy M. Jaeggi
Reuss River plunging into Lake Lucerne,
Switzerland: flood of summer, 2005
1
GRAIN SIZE CLASSIFICATION


D2 2
n(D)
    og2 (D) 
n(2)
Type
D (mm)


Notes
Clay
< 0.002
< -9
>9
Usually cohesive
Silt
0.002 ~ 0.0625 -9 ~ -4
4~9
Cohesive ~ noncohesive
Sand
0.0625 ~ 2
-4 ~ 1
-1 ~ 4
Non-cohesive
Gravel
2 ~ 64
1~6
-6 ~ -1
“
Cobbles
64 ~ 256
6~8
-8 ~ -6
“
>8
< -8
“
Boulders > 256
Mud = clay + silt
2
SEDIMENT FALL VELOCITY IN STILL WATER
R f  f (Re p )
where
vs
Rf 
RgD
RgD D
Re p 

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):
R f  exp { b1  b2 n (Re p )  b3 [n (Re p )] 2
 b4 [n (Re p )]  b5 [n (Re p )] }
3
4
b1
2.891394
b2
0.95296
b3
0.056835
b4
0.002892
b5
0.000245
The original relation also includes a correction for shape.
3
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
4
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.
5
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.
6
VIDEO CLIP ILLUSTRATING BEDLOAD IN A MODEL
RIVER IN THE LABORATORY
Wong et al. (2007)
7
VIDEO CLIP ILLUSTRATING BEDLOAD AND
SUSPENDED LOAD CARRIED NEAR THE BED OF
THE TRINITY RIVER, CALIFORNIA
8
Clip courtesy A. Krause
VIDEO CLIP ILLUSTRATING BEDLOAD AND
SUSPENDED LOAD CARRIED BY A TURBIDITY
CURRENT
Cantelli et al. (2008)
9
APPLICATION TO TURBIDITY CURRENTS
RIVER: The downslope component of gravitational force Fgd
acting on the control volume to drive the flow is
Fgd  w (1 Rc )gLAS
TURBIDITY CURRENT: The downslope component of gravitational
force Fgd acting on the control volume to drive the flow is
A
Fgd  wRcgLAS
L
where c is the volume
concentration of suspended
sediment
a
S  tan(a)
10
CRITICAL ROLE OF SUSPENDED SEDIMENT TO
DRIVE TURBIDITY CURRENTS
RIVER: Suspended sediment is NOT NECESSARY to drive
the flow.
Fgd  w (1 Rc )gLAS
TURBIDITY CURRENT: Suspended sediment is NECESSARY to
drive the flow!
A
Fgd  wRcgLAS
L
The suspended sediment in
turbidity currents is composed of
mud and/or sand.
a
S  tan(a)
11
BEDLOAD TRANSPORT BY TURBIDITY CURRENTS
Turbidity currents can transport sand,
and sometimes gravel as bedload.
The same size of sand can
participate in both transport
mechanisms, whereas gravel is
usually moved only 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
12
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.
Gravel/sand deposit
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.)
13
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.
14
BEDLOAD AND SUSPENDED LOAD IN AN
EXPERIMENTAL DELTA WITH A PLUNGING
TURBIDITY CURRENT
Kostic and Parker (2003)
15
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 sedimentwater 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
X
c  1x10
R 1
6
Conversion from X to c
R
X
c
1.65
2000 mg/liter
0.000755
Double-click to open the
spreadsheet.
16
A GARDEN-VARIETY SAND-BED RIVER: THE
MINNESOTA RIVER NEAR MANKATO
17
Image courtesy P. Belmont
SUSPENDED SEDIMENT CONCENTRATION IN A
GARDEN-VARIETY RIVER
Suspended Sediment Concentration Minnesota River
Mankato
10000
X mg/liter
1000
100
Note: X is never
higher than ~ 3000
mg/l
10
1
1
Q = flow discharge
10
100
Q (m3/s)
1000
10000
18
SUSPENDED SEDIMENT CONCENTRATION IN A
GARDEN-VARIETY RIVER contd.
Suspended Sediment Concentration Minnesota River
Mankato
Note: c is never higher than
~ 0.001:
highly dilute suspension
1
0.1
c
0.01
c = 1E-05(Q)0.388
0.001
0.0001
0.00001
0.000001
1
10
100
Q (m3/s)
1000
10000
19
BED GRAIN SIZE DISTRIBUTION IN A GARDENVARIETY RIVER
Bed Grain Size Distributions, Minnesota River at Mankato
100
90
GSD1
GSD2
GSD3
GSD4
GSD5
GSD6
GSD7
GSD8
GSD9
GSD10
GSD11
GSD12
GSD13
Average
Percent Finer
80
70
60
Where’s the mud?
50
40
30
20
10
0
0.01
0.1
1
D (mm)
10
100
20
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
100
Fload<62 = [-0.0245(Q) + 87.828]/100
90
Percent mud
80
70
60
50
The suspended load
is mostly mud!
40
30
20
10
0
0
200
400
600
Q (m3/s)
800
1000
1200
21
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.
22
THE CASCADIA
AND ASTORIA
SUBMARINE
CHANNELS OFF
THE PACIFIC
COAST OF THE
USA
Nelson et al., 2000
23
CORES SHOW THAT THE CHANNELS MOVE MUD,
SAND AND GRAVEL TO DEEP WATER
Nelson et al., 2000
24
RIVERS AND FLOODPLAINS
Strickland River, New Guinea
Mostly mud-free channel,
Mud-rich floodplain (but with sand also)
25
Image courtesy J. W. Lauer
RIVERS AND FLOODPLAINS
Minnesota River, Minnesota
Sand load moves as bedload and
suspended load. Exchanges mostly with
bed, but with floodplain as well.
Image courtesy J. W. Lauer
Mud moves as suspended wash load. 26
Exchanges with the floodplain.
SAND AND MUD
Sand rich
Mud rich
Paraná River, Argentina
27
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)
28
SCALE FOR GRAVITATIONAL FORCE:
RIVERS AND TURBIDITY CURRENTS
flow
amb
U
C
R
H
Wimm
=
=
=
=
=
=
=
denote the density of the flowing
density of the ambient fluid
flow velocity
volume concentration of suspended sediment
(sed - f)/f = submerged specific gravity of sediment
depth (layer thickness) and width of control volume
immersed weight in control volume
ambient fluid
Wimm  flow  amb gH3
H
H
Flowing fluid
29
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
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
Wimm  w (1 RC)  air gH3
Wimm  w (1 RC)  w gH3
ambient fluid
H
H
H
Flowing fluid
30
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
A
U
x
Ut
UtA
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.
31
VOLUME, MASS AND MOMENTUM DISCHARGE contd.
The discharge of any quantity is the rate at which it crosses a section per
unit time
A
U
x
Ut
UtA
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
32
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:
Control volume
/t(x-momentum in c.v.) =
Inflow rate – outflow rate – Finert
Finert
Steady flow: no outflow of xmomentum:
0  flow U2A  0  Finert
Finert  flow U A
2
x
33
THE DENSIMETRIC FROUDE NUMBER:
A SCALE OF THE RATIO OF INERTIAL TO GRAVITATIONAL
FORCES
Finert  flow U H
2
2
Wimm  flow  amb gH3
Densimetric Froude number Frd:
2 2
F

U
H
2
inert
flow
Frd 


3
Wimm ( flow  amb )gH
 flow U
( flow  amb )gH
ambient fluid
H
2
H
H
Flowing fluid
34
THE DENSIMETRIC FROUDE NUMBER:
RIVER AND TURBIDITY CURRENT
flow  w (1 RC) , amb  air
RIVER:
Now for R ~ 1.65, C << 1 and air/w << 1,
w (1  RC )U
U
Fr 

w (1 RC )  air )gH gH
2
2
2
d
TURBIDITY CURRENT:
flow  w (1 RC) , amb  w
Now for R ~ 1.65 and C << 1,
w (1 RC )U
U
Fr 

w (1 RC)  w )gH RCgH
2
2
d
2
35
THE FROUDE NUMBERS:
RIVER:
U
Frd  Fr 
gH
TURBIDITY CURRENT:
U
Frd 
RCgH
Most of the concepts based on Froude number for open channel (river) flow
generalize to turbidity currents!
Frd < 1: subcritical (tranquil) flow
Frd = 1: critical flow
Frd > 1: supercritical (shooting) flow
36
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 > 1
Sangamon River, Illinois; Fr << 1
37
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
38
Image courtesy N. Strong
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)
39
BED SHEAR STRESS AND FLOW VELOCITY
For simplicity, approximate a river as having a wide, rectangular crosssection, so that B/H >> 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
Cf 
b
U2
40
SHEAR VELOCITY AND DIMENSIONLESS CHEZY
RESISTANCE COEFFICIENT
The shear velocity u [L/T] is defined as
u 
b

The dimensionless Chezy resistance coefficient Cz is defined as
Cz 
U
u
41
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]
x
bBx
x

H
B
gHxBS
The bed slope angle  of the great
majority of alluvial rivers is sufficiently
small to allow the approximations
sin   tan   S , cos  1
42
THE DEPTH-SLOPE RELATION FOR NORMAL OPENCHANNEL FLOW
Conservation of water mass (= conservation of water volume as water
can be treated as incompressible):
qw  UH
Qw  qwB  UHB
Conservation of downstream momentum:
Impelling force (downstream component of weight of water) =
resistive force
gHBx sin  gHBxS  bBx
Reduce to obtain depth-slope
product rule for normal flow:
b  gHS
u  gHS
x
bBx
x

H
B
gHxBS
43
FLOW REYNOLDS NUMBER, SHIELDS NUMBER
AND DIMENSIONLESS CHEZY NUMBER
44
CRITERIA FOR THE ONSET OF MOTION AND SIGNIFICANT
SUSPENSION
45
THE SHIELDS DIAGRAM
46
THE DEPTH-SLOPE RELATIONSHIP FOR SHEAR STRESS IN
RIVERS
47
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.

Qbf
Minnesota River and
floodplain, USA, during the
record flood of 1965
Q
48
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]
49
FROUDE NUMBER AT BANKFULL FLOW
50
DIMENSIONLESS CHEZY RESISTANCE COEFFICIENT AT
BANKFULL FLOW
51
BANKFULL FLOW AND THE SHIELDS DIAGRAM
52
VELOCITY AND SUSPENDED SEDIMENT PROFILES IN A
RIVER
53
COMPARISON BETWEEN RIVERS AND TURBIDITY
CURRENTS
54
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, 606623.
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?????
55