LECTURE 5 CONCEPTS FROM RIVERS THAT CAN BE APPLIED TO TURBIDITY CURRENTS

1. 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

2. GRAIN SIZE CLASSIFICATION Mud = clay + silt

3. 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.

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) The calculations to the left were performed withRTe-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 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.

7. VIDEO CLIP ILLUSTRATING BEDLOAD IN A MODEL RIVER IN THE LABORATORY Wong et al. (2007)

8. VIDEO CLIP ILLUSTRATING BEDLOAD AND SUSPENDED LOAD CARRIED NEAR THE BED OF THE TRINITY RIVER, CALIFORNIA Clip courtesy A. Krause

9. VIDEO CLIP ILLUSTRATING BEDLOAD AND SUSPENDED LOAD CARRIED BY A TURBIDITY CURRENT Cantelli et al. (2008)

10. 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

11. 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.

12. 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

13. 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.

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)

16. 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.

17. A GARDEN-VARIETY SAND-BED RIVER: THE MINNESOTA RIVER NEAR MANKATO Image courtesy P. Belmont

18. SUSPENDED SEDIMENT CONCENTRATION IN A GARDEN-VARIETY RIVER Note: X is never higher than ~ 3000 mg/l Q = flow discharge

19. SUSPENDED SEDIMENT CONCENTRATION IN A GARDEN-VARIETY RIVER contd. Note: c is never higher than ~ 0.001: highly dilute suspension

20. BED GRAIN SIZE DISTRIBUTION IN A GARDEN-VARIETY RIVER Where’s the mud?

21. FRACTION OF SUSPENDED LOAD THAT IS MUD IN A GARDEN-VARIETY RIVER The suspended load is mostly mud!

22. 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.

23. THE CASCADIA AND ASTORIA SUBMARINE CHANNELS OFF THE PACIFIC COAST OF THE USA Nelson et al., 2000

24. CORES SHOW THAT THE CHANNELS MOVE MUD, SAND AND GRAVEL TO DEEP WATER Nelson et al., 2000

25. RIVERS AND FLOODPLAINS Strickland River, New Guinea Mostly mud-free channel, Mud-rich floodplain (but with sand also) Image courtesy J. W. Lauer

26. 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

27. SAND AND MUD Sand rich Mud rich Paraná River, Argentina

28. 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)

29. 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

30. 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 ambient fluid H H H Flowing fluid

31. A U UtA x Ut 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.

32. A U UtA x Ut 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

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.) Force balance: /t(x-momentum in c.v.) = Inflow rate – outflow rate – Finert Steady flow: no outflow of x-momentum: Control volume Finert x

34. 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

35. THE DENSIMETRIC FROUDE NUMBER: RIVER AND TURBIDITY CURRENT RIVER: Now for R ~ 1.65, C << 1 and air/w << 1, TURBIDITY CURRENT: Now for R ~ 1.65 and C << 1,

36. THE FROUDE NUMBERS: RIVER: TURBIDITY CURRENT: 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

37. 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

38. Water surface internal hydraulic jump 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 < 1Supercritical: Frd > 1 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, 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

41. 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

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] 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

43. 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:

44. FLOW REYNOLDS NUMBER, SHIELDS NUMBER AND 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 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] 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]

50. FROUDE NUMBER AT BANKFULL FLOW