1. 1 LECTURE 11 INTRODUCTION TO TURBIDITY CURRENT MORPHODYNAMICS CEE 598, GEOL 593 TURBIDITY CURRENTS: MORPHODYNAMICS AND DEPOSITS 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) bed saline underflow ambient fresh water

2. 2 THE CASE OF RUPERT INLET From Poling et al. (2002) 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.

3. 3 THE CASE OF RUPERT INLET contd. Photo: http://gateway.uvic.ca/archives/featured_collections/esa/fonds_island_copper_mines/default.html 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.

4. 4 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)

5. 5 THE TURBIDITY CURRENT FORMED AN EXTENDED MEANDERING CHANNEL From Hay (1987b) meander bends channel axis

6. 6 LONG PROFILE, RELIEF AND WIDTH OF THE CHANNEL Relief ~ vertical distance from levee top to channel bottom ~ channel depth. From Hay (1987b)

7. 7 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)

8. 8 THE ACOUSTIC IMAGING SHOWED MORPHODYNAMICS IN ACTION! 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. channel bed fish! approximate interface of turbidity current

9. 9 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.

10. 10 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.

11. 11 x = nearly horizontal boundary-attached “streamwise” coordinate [L] z = nearly vertical coordinate upward normal from boundary [L] 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.

12. 12 1D EXNER EQUATION FOR THE CONSERVATION OF BED SEDIMENT: SOME PARAMETERS Parameters: q s = volume suspended load transport rate per unit width [L 2 T -1 ] = UCH q b = volume bedload transport rate per unit width [L 2 T -1 ]  s = sediment density [ML -3 ] v s = 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/T 2 ] t = time [T]

13. 13 1D EXNER EQUATION FOR THE CONSERVATION OF BED SEDIMENT; DERIVATION E s = v s E s = volume rate per unit time per unit bed area that sediment is entrained from the bed into suspension [LT -1 ]. D s = v s r o C = 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

14. 14 REDUCTION OF THE EXNER EQUATION Since E s = v s E and D s =v s r o C, the equation reduces to: Compare this relation with the equation of consevation of suspended sediment: Since q s = 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 << 1)

15. 15 COUPLING OF THE EXNER EQUATION TO THE EQUATIONS GOVERNING THE FLOW Example: 3-equation model: where the closure relations are:

16. 16 THE QUASI-STEADY ASSUMPTION Turbidity currents are dilute suspensions of sediment. As a result, the volume suspended sediment discharge per unit width q s = UHC is much smaller than the water discharge per unit width q w = UH (since C << 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.

17. 17 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:

18. 18 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 C i, so that the total concentration C T is given as: The volume suspended load transport rate per unit width q si and the fraction of sediment in the suspended load in the ith grain size range p si 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 L s 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 F i

19. 19 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 q bi and p bi, where The volume rates per unit time per unit bed area E si and D si of erosion into suspension and deposition from suspension are given as where v si is the fall velocity for the ith grain size range, E usi is a unit entrainment rate for the ith grain size range, and r oi = c bi /C i, where c bi is the near-bed concentration in the ith grain size range.

20. 20 1D EXNER EQUATION FOR MIXTURES The equation takes the form where f Ii 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

21. 21 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:

22. 22 INTERFACIAL EXCHANGE FRACTIONS f Ii Closure relations for f Ii, r oi E si and q bi need to be specified in order to implement the formulation for mixtures. The substrate fractions below the surface layer are denoted as f i. Note that f i 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.

23. 23 THE PARAMETER E usi Garcia and Parker (1991) generalized their relation for entrainment in rivers to sediment mixtures. The relation for mixtures takes the form where D i denotes the characteristic grain size of the ith range and D 50 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 S e is an energy slope. Both these relations apply only to non- cohesive sediment, and have not been verified for turbidity currents.

24. 24 THE PARAMETERS r oi AND q bi The parameter r oi 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

25. 25 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: LINKAGE TO THE EQUATIONS OF MOTION

26. 26 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.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.

27. 27 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.