INTRODUCTION TO TURBIDITY CURRENT MORPHODYNAMICS

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CEE 598, GEOL 593 TURBIDITY CURRENTS
MORPHODYNAMICS AND DEPOSITS
LECTURE 11 INTRODUCTION TO TURBIDITY CURRENT
MORPHODYNAMICS
ambient fresh water
saline underflow
bed
Top photo showing the deposit of lightweight
plastic sediment formed by the repeated passage
of saline underflows (analogs of turbidity
currents). Left time evolution of the
bed. From Spinewine et al. (submitted)
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THE CASE OF RUPERT INLET
The Island Copper Mine, Vancouver Island, British
Columbia, was in operation from 1970 to 1995. To
deal with the massive amounts of mine tailings (
waste crushed rock) produced, Island Copper Mine
discharged around 400 million tons of tailings
through an outfall at 50 m depth into the
adjacent Rupert Inlet.
From Poling et al. (2002)
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THE CASE OF RUPERT INLET contd.
The tailings (ground up rock), were 40 fine to
very fine sand, and 60 silt, with a median
size 30 ?m. They were disposed continuously to
form a turbidity current that was sustained for
decades.
Photo http//gateway.uvic.ca/archives/featured_co
llections/esa/fonds_island_copper_mines/default.ht
ml
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THE REAL-TIME CONSTRUCTION OF A MINI-SUBMARINE FAN
Monitoring of the tailings disposal allowed for
one of the first cases where the evolution of
morphology due to turbidity currents was
monitored in real time (Hay, 1987a,b).
From Hay (1987a)
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THE TURBIDITY CURRENT FORMED AN EXTENDED
MEANDERING CHANNEL
channel axis
meander bends
From Hay (1987b)
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LONG PROFILE, RELIEF AND WIDTH OF THE CHANNEL
Relief vertical distance from levee top to
channel bottom channel depth.
From Hay (1987b)
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THE CHANNEL SHOWED WELL-DEVELOPED CONSTRUCTIONAL
LEVEES
The acoustic image shows the channel
cross-section at site 67, located below. Flow
direction is out of the page.
From Hay (1987b)
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THE ACOUSTIC IMAGING SHOWED MORPHODYNAMICS IN
ACTION!
fish!
approximate interface of turbidity current
channel bed
From Hay (1987b)
The turbidity current is overbanking due to
superelevation at the outside of a bend. This
overbanking has caused the outer bank to become
higher than the inner bank. Flow direction is
out of the page.
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BEDLOAD AND SUSPENDED LOAD
Bed material load is that part of the sediment
load that exchanges with the bed (and thus
contributes to morphodynamics). 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. 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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TURBIDITY CURRENTS MAY CARRY BEDLOAD, BUT THEY
MUST BE DOMINATED BY SUSPENDED LOAD
Rivers are driven by the downstream pull of
gravity on the water. The water then pulls the
sediment with it. The sediment can move
predominantly as bedload, predominantly as
suspended load or some combination
thereof. Turbidity currents are driven by the
downstream pull of gravity on the suspended
sediment. The suspended sediment then pulls the
water with it. The resulting flow can then move
bedload as well. A turbidity current cannot be
driven by bedload alone, because the bedload is
a) supported essentially by collisions with the
bed, not turbulence and b) moves in a very thin
layer very close to the bed.
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BOUNDARY-ATTACHED COORDINATE SYSTEM
We assume a bed that is sloping only modestly in
the streamwise direction. The parameter x is
parallel to the bed and the parameter z is upward
normal to the bed.

• x nearly horizontal boundary-attached
  streamwise coordinate L
• z nearly vertical coordinate upward normal from
  boundary L

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1D EXNER EQUATION FOR THE CONSERVATION OF BED
SEDIMENT SOME PARAMETERS

• Parameters
• qs volume suspended load transport rate per
  unit width L2T-1 UCH
• qb volume bedload transport rate per unit width
  L2T-1
• ?s sediment density ML-3
• vs sediment fall velocity
• bed elevation L
• ?p porosity of sediment in bed deposit 1
• (volume fraction of bed sample that is holes
  rather than sediment
• 0.25 0.55 for noncohesive material, larger for
  cohesive material)
• g acceleration of gravity L/T2
• t time T

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1D EXNER EQUATION FOR THE CONSERVATION OF BED
SEDIMENT DERIVATION
Es vsEs volume rate per unit time per unit
bed area that sediment is entrained from the bed
into suspension LT-1. Ds vsroC volume rate
per unit time per unit bed area that sediment
is deposited from the water column onto the bed
LT-1.
Time rate of change of sediment mass in control
volume deposition rate from suspension
erosion rate into suspension net inflow rate of
bedload
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REDUCTION OF THE EXNER EQUATION
Since Es vsE and Ds vsroC, the equation
reduces to Compare this relation with the
equation of consevation of suspended
sediment Since qs UCH, the Exner equation
can be rewritten as The last term can be
usually neglected because the mass stored as
suspended sediment per unit volume is negligible
compared to the mass of sediment stored per unit
volume in the bed (C ltlt 1)
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COUPLING OF THE EXNER EQUATION TO THE EQUATIONS
GOVERNING THE FLOW
Example 3-equation model
where the closure relations are
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THE QUASI-STEADY ASSUMPTION
Turbidity currents are dilute suspensions of
sediment. As a result, the volume suspended
sediment discharge per unit width qs UHC is
much smaller than the water discharge per unit
width qw UH (since C ltlt 1). Under these
conditions, the morphodynamics of sustained
turbidity currents can often be simplified using
the quasi-steady approximation (de Vries,
1965) The quasi-steady assumption
cannot be used for flows that develop rapidly in
time, such as a surge-type turbidity current.
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FLOW OF CALCULATION USING THE QUASI-STEADY
APPROXIMATION
The bed profile ?(x) is known at time t Compute
S - ??/?x Compute the flow over this bed by
solving the equations below Once U, C and
H are known, compute the new bed profile at t
?t by solving the Exner equation
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GENERALIZATION OF THE FORMULATION FOR SEDIMENT
SIZE MIXTURES
We divide the range of grain sizes into N bins I
1 to N. The volume concentration of suspended
sediment in each bin is Ci, so that the total
concentration CT is given as The volume
suspended load transport rate per unit width qsi
and the fraction of sediment in the suspended
load in the ith grain size range psi are
Using the active layer concept introduced in
Chapter 4 of Parker (2004 e-book), the bed is
divided into a surface active layer of thickness
Ls and a substrate below. The surface has no
vertical structure the fraction of sediment in
the ith grain size range in the bed surface is Fi
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GENERALIZATION OF THE FORMULATION FOR SEDIMENT
SIZE MIXTURES contd.
We further define the volume bedload transport
per unit and the fraction bedload in the ith
grain size as qbi and pbi, where The volume
rates per unit time per unit bed area Esi and Dsi
of erosion into suspension and deposition from
suspension are given as
where vsi is the fall velocity for the ith grain
size range, Eusi is a unit entrainment rate for
the ith grain size range, and roi cbi/Ci, where
cbi is the near-bed concentration in the ith
grain size range.
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1D EXNER EQUATION FOR MIXTURES
The equation takes the form where fIi denotes
the fraction in the ith range of the sediment
that interchanges between the surface layer and
the substrate below as the bed aggrades or
degrades. Reducing with the forms below,
it is found that
surface layer
substrate
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REDUCTION OF THE EXNER EQUATION FOR MIXTURES
By definition, Summing over all grain sizes
yields the Exner formulation for bed
evolution. Between the second and third
equations above the following equation can be
derived for the time evolution of the grain size
distribution of the surface layer
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INTERFACIAL EXCHANGE FRACTIONS fIi
Closure relations for fIi, roi Esi and qbi need
to be specified in order to implement the
formulation for mixtures. The substrate
fractions below the surface layer are denoted as
fi. Note that fi can vary as a function of
elevation within the substrate z, so reflecting
the stratigraphic architecture of the deposit.
where 0 ? ? ? 1 (Hoey and Ferguson, 1994
Toro-Escobar et al., 1996). That is The
substrate is mined as the bed degrades. A mixture
of surface and bedload material is transferred to
the substrate as the bed aggrades, making
stratigraphy. Stratigraphy (vertical variation
of the grain size distribution of the substrate)
needs to be stored in memory as bed aggrades in
order to compute subsequent degradation.
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THE PARAMETER Eusi
Garcia and Parker (1991) generalized their
relation for entrainment in rivers to sediment
mixtures. The relation for mixtures takes the
form where Di denotes the characteristic
grain size of the ith range and D50 is a median
size of the sediment in the active layer. Wright
and Parker (2004) amended the above relation so
as to apply to larger scale. as well as the types
previously considered by Garcia and Parker
(1991). The relation is the same as that of
Garcia and Parker (1991) except for the following
amendments where Se is an energy slope.
Both these relations apply only to non-cohesive
sediment, and have not been verified for
turbidity currents.
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THE PARAMETERS roi AND qbi
The parameter roi is not very well constrained
for turbidity currents. In the lack of an
alternative, the relation given in Lecture 8 can
be generalized to mixtures as This relation
was introduced by Parker (1982) based on the
vertical distribution of suspended sediment in a
river proposed by Rouse (1939). A review of
bedload transport relations for sediment mixtures
is given in Parker (2004, e-book). A sample
relation is that of Ashida and Michiue (1972)
where
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LINKAGE TO THE EQUATIONS OF MOTION
In order to link to the Exner formulation for
sediment mixtures, the equations of motion need
to be modified in a straightforward way. In the
case of the 3-equation model, the equations
become In the 4-equation model, the
equation for K generalizes to
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REFERENCES
Ashida, K. and M. Michiue, 1972, Study on
hydraulic resistance and bedload transport rate
in alluvial streams, Transactions, Japan Society
of Civil Engineering, 206 59-69 (in
Japanese). García, M., and G. Parker, 1991,
Entrainment of bed sediment into suspension,
Journal of Hydraulic Engineering, 117(4)
414-435. Hay, A. E., 1987, Turbidity currents and
submarine channel formation in Rupert Inlet,
British Columbia, Canada 1. Surge observations.
Journal of Geophysical Research, 92(C3),
2975-2881. Hay, A. E., 1987, Turbidity currents
and submarine channel formation in Rupert Inlet,
British Columbia, Canada 1. The roles of
continuous and surge-type flow. Journal of
Geophysical Research, 92(C3), 2883-2900. Hoey, T.
B., and R. I. Ferguson, 1994, Numerical
simulation of downstream fining by selective
transport in gravel bed rivers Model development
and illustration, Water Resources Research, 30,
2251-2260. Parker, G., 1982, Conditions for the
ignition of catastrophically erosive turbidity
currents. Marine Geology, 46, pp. 307-327,
1982. Parker, G., 2004, ID Sediment Transport
Morphodynamics, with applications to Fluvial and
Subaqueous Fans and Fan-Deltas,
http//cee.uiuc.edu/people/parkerg/morphodynamics
_e-book.htm . Poling, G. W., Ellis, D. V.,
Murray, J. W., Parsons, T. R. and Pelletier, C.
A., 2002, Underwater tailing placement at Island
Copper Mine A Success Story. SME, 216 p. Rouse,
H., 1939, Experiments on the mechanics of
sediment suspension, Proceedings 5th
International Congress on Applied Mechanics,
Cambridge, Mass,, 550-554.
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REFERENCES contd.
Spinewine, B., Sequeiros, O. E., Garcia, M. H.,
Beaubouef, R. T., Sun, T., Savoye, B. and Parker,
G., Experiments on internal deltas created by
density currents in submarine minibasins. Part
II Morphodynamic evolution of the delta and
associated bedforms. submitted 2008,
Sedimentology. Toro-Escobar, C. M., C. Paola, G.
Parker, P. R. Wilcock, and J. B. Southard, 2000,
Experiments on downstream fining of gravel. II
Wide and sandy runs, Journal of Hydraulic
Engineering, 126(3) 198-208. de Vries, M. 1965,
Considerations about non-steady bed-load
transport in open channels. Proceedings, 11th
Congress, International Association for Hydraulic
Research, Leningrad 381-388. Wright, S. and G.
Parker, 2004, Flow resistance and suspended load
in sand-bed rivers simplified
stratification model, Journal of Hydraulic
Engineering, 130(8), 796-805.