Sediment Transport (in Estuaries)

Transcription

1 Sediment Transport (in Estuaries)

2 Modes of Sediment Transport An incomplete introduction to: Bed Load Suspended Load Instrumentation and Challenges

3 Rouse Parameter, P Suspended load: w s κu * < 0.8 Rouse Parameter, P Bedload: w s κu * > 2 Open University, 1999

4 Middleton and Southard 1984

5 Consider steady horizontally uniform flow. Estimate stress at the bed: Law of the Wall u u * 1 = ln κ z z 0 Drag Coefficient 2 τ b = ρc D u 100 Reynolds Stresses τ = ρu ' w ' u z,u 100,u w u *, τ 0 τ c suspended load bed load

6 How to find w s? A force balance leads to Stokes Law C D = 24 Re F D = C D U ρ 2 2 A π 3 Fg = d ( ρs ρ) g 6 u Re = = w ud ν s = F F C = drag force = gravitational force = drag coefficient ρ, ρ = density of s A = area of d D g D sphere = diameter of water, sediment sphere g = acceleration due to gravity ν = ( ρs ρ) 18μ μ ρ gd 2

7 Bed Load w s Rouse Parameter > 2 κ u * q b = 8[ Ψ( t) Ψ ] 2 ( ρ ρ s cr ) g Recall critical Shield s parameter: Wright After Meyer-Peter and Muller (see Wright 1995) Ψ cr = gd s τ cr ρs ρ( 1) ρ

8 Bedload 3 q b αu * q b =bedload transport rate Rate of bedload depends on power, i.e. rate of flow doing work on sediment Energy ~ velocity 2 Power=energy x velocity Power ~ velocity 3 Can lead to fractionation and sorting by size, transport of different sizes at different phases of tide, net fluxes Open University 1999

9 Bedforms Result of bedload, tight feedback, affect partitioning of form drag and skin friction Relatively low Froude numbers, eventually as Fr increases, bedforms wash out, create plain bed Open University 1999

10 Instrumentation: Fan beam, imaging sonar and poking eyeball Sherwood, Rubin, USGS

11 Rouse Parameter, P Suspended load: w s κu * < 0.8 Rouse Parameter, P Bedload: w s κu * > 2

12 Suspended Sediment Transport Equation (Sediment Mass Balance) C t + U C x i = x i C ( K s ) ( wsc) x z advection mixing settling i U, flow velocity U(x,y,z,t) C, susp sed conc C(z,C n ) K s, eddy diffusivity, K s (ht above bed, z, boundary sheer stress, τ b,u * roughness, k s stratification ρ/ z, ρ(s,t,c)) w s, particle settling velocity w s (diameter D, density, ρ, ρ s )) Need to measure flow, fluid, sediment

13 Suspended Sediment Transport 0 (steady) 0 C t = z ( K s C z ) + _ u C x + w s C z : Entrainment/Mixing s 2: Advection z 3: Depostion by Settling = βκu z(1 z / ) K s K C s = w C * h C = C a at z=z a

14 Rouse Equation: Vertical Distribution of Suspended Sediments C C C C h = total water depth w u * s z a z a h z = ( z za h z = conc at ht above bed z = conc at ht above bed a = settling velocity = shear velocity κ = von karman constant, 0.41 a ) w κu s * P Geyer 1993

15 C C z a h = ( z z z h a z a ) ws κu *

16 What do we need to know? 0.41 von karman constant, shear velocity settling velocity water depth total conc at ht above bed conc at ht above bed ) ( * * = = = = = = = κ κ u w h a C z C z h z z z h C C s a z u w a a a z s Geyer 1993

17 Shear Velocity (forcing) Law of the Wall u u * 1 = ln κ z z 0 Drag Coefficient 2 τ b = ρc D u 100 Reynolds Stresses τ = ρu ' w '

18 C t + U C x i = x i C ( K s ) ( w sc ) x z i Boundary Layer Tripods Eddy Diffusivity K s function of: boundary sheer stress,τ b, U * due to currents (commonly measured by u/ z or <u w >) AND waves Also roughness, stratification PCADP u/ z P ABS C/ z ADV <u w > Thanks Sherwood, USGS

19 C t + U C x i = x Flow Measurements (Eulerian): i C ( K s ) ( wsc) x z i U, flow velocity U(x,y,z,t) C, susp sed conc C(z,C n ) K s, eddy diffusivity, K s (ht above bed, z, boundary sheer stress, τ b,u * roughness, ks stratification ρ/ z, ρ(s,t,c)) w s, particle settling velocity w s (diameter d, density, ρ, ρ s )) At a point: Mechanical Rotors Electromagnetic Current Meters Acoustic Doppler Velocimeter Through the water column: Acoustic Doppler Current Profiler

20 Settling velocity - a big challenge for cohesive sediments In the marine environment fine particles interact to flocculate, aggregate, agglomerate Floc pictures from Tim Milligan

21 Wash load 500μ w s fine sand

22 Cohesive Sediments Clay particles d<2um, plate-like Surfaces have charges, electrostatic forces Comparable to gravity Clay particles stick together (cohesion, stickiness) Becomes significant when 5-10% clay by weight

23 Flocculation, aggregation, agglomeration Face of platelet generally ve charge In salt water double layer is suppressed Electrostatic charge repulses V R 1/e R Van der Waals attractive V A 1/R 2 Fresh water: repulsive dominates Salt water: reduces surface charge, V A dominates Flocculation begins psu Organic matter enhances Flocculation less effective ast

24 How to bring particles together? 1. Brownian motion collision rate of frequency 4ΚTn K B = 3μ K T n = = = μ = Boltzmann's constant temperature number of particles molecular viscosity Maybe effective at high conc of small particles (d<0.5μ), otherwise considered insignificant What is it a function of?

25 2. Shear K v R du dz 4 3 = nr 3 = sum of = What is it a function of? du dz radii velocity gradient Effective with large particles at small shear, or small particles at large shear K v >K B

26 3. Differential Settling What is it a function of? K s απr 2 Δwn R = sum of radii Δw = relative settling vel Not very effective

27 4. Encounters due to turbulent shear ε 3 K i = 1.294R ( ) n1n2 ν ε = turbulent dissipation rate Effect of Turbulence 1 2 What is it a function of? D f G=rms vel grad

28 G=rms vel grad ~c gel Ross and Mehta, 1989 D f

29 Flocs have odd shapes, grow and break up with changing concentration and shear, and have variable density What do you use for settling velocity?

30 C t + U C x i = x i C ( K s ) ( wsc) x z i w s, particle settling velocity w s (diameter D, density ρ, ρ s ρ f ) Stokes calculation for sphere (problematic for fine sediments) Estimate from in situ images and assumed density Measure directly Lots of examples of optical, laser, settling, capture and bottom withdrawal Milligan

31 INSSECT IN situ Size and SEttling Column Tripod Digital floc camera MAVS Recovery package OBS Video Camera & settling column Fins Sediment trap Rotating frame Thanks Mikkelsen, Milligan, Hill

32 Try to model: See Winterwerp and van Kesteren 2004 for description of flocculation model based on fractal structure of flocs. Can determine equilibrium floc diameter, D f, and differential (excess) density, Δρ f Balance between gravitational and drag forces: π 3 1 π 2 2 Fg = α D f gδρ f Fd = βcd ρw D f ws, f p p C D = ( Re Re ) Based on empirical data w s, f = 1 f α ( ρs ρw) g 3 n D f f Dp 18β μ Re f n α and β are coefficients depending on shape (sphericity) n f is the fractal dimension varying from ~1.4 (marine snow) to for estuarine and coastal waters. n f =2 yields good results for the Ems estuary D f, D p are diameter of floc and primary particle For α=β=1 and n f =3 you get Stokes

33 Winterwerp and van Kesteren 2004 Results in pretty typical values. See Hill 1998 and other work by Hill, Milligan, Fox, and others. In practice For fine silt and clay fraction one assumes a floc fraction and assigns a floc settling velocity of ~1 mm/sec.

34 Reference Concentration, C a Measure directly Calculated from excess shear stress Erosion rate Latter two are function of bed characteristics

35 Reference concentration, C a, for size class j of bed sediment, C b, a function of excess shear stress, θ. γ is and empirical constant. C a = C, j b, j γθ j 1+ γθ j θ j = τ τ τ cr cr, j Wright 1995

36 Challenges: For cohesive sediments τ c varies with depth (and therefore time) Winterwerp and van Kesteren 2004 Dyer 1986

37 C + U t C x i = x i C ( K s ) ( wsc) x z Suspended Sediment Concentration At a point: Discrete samples with a bottle or pump, filter and weigh i U, flow velocity U(x,y,z,t) C, susp sed conc C(z,C n ) K s, eddy diffusivity, K s (ht above bed, z, boundary sheer stress, τ b,u * roughness, ks stratification ρ/ z, ρ(s,t,c)) w s, particle settling velocity w s (diameter d, density, ρ, ρ s )) At a point, continuous in time, (quasiinstantaneous depth profile): Optical (e.g. transmissometer, OBS) Through the water column: Acoustic (e.g. ABS (near bottom), ADCP) Fine sediments: changing particle characteristics

38 Profiling Tripod Salinity Temperature Pressure Current Speed and Direction Optical Backscatter (C) Water Samples

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40 Effects, Issues, Challenges Simplest case: = K w s flocs, hindered settling K s = eddy diffusivity K s =K(stratification, Ri correction), w s C s C z Would like to know how stratification changes through the water column, with time.

41 Autonomous Profiler Submersible programmable winch with buoyant instrument package Seabird Seacat with Optical Backscatterance Sensor Hourly profiles

42 T (degc) mab Autonomous Profiler MVCO 09/04 09/ SSC mab and wave ht m 09/04 09/

43 4 wvht (m), C1 mg/l* /03 09/04 09/05 09/06 09/07 09/08 09/09 09/10 09/11 09/12 09/13 22 T10 and T1 (deg C) /03 09/04 09/05 09/06 09/07 09/08 09/09 09/10 09/11 09/12 09/13

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45 High Concentration Suspensions

46 Rouse Equation: Vertical Distribution of Suspended Sediments C C C C h = total water depth w u * s z a z a h z = ( z za h z = conc at ht above bed = conc at ht above bed = settling velocity = shear velocity κ = von karman constant, a ) w κu s * P z a 0.41 Geyer 1993

47 SSC distribution and flux based on Rouse equation (steady, horizontally uniform) w κu q s s * < 0.8 = u z c z dz These profiles don t look like law of the wall or Rouse.

48 Kirby and Parker 1983

49 Kineke et al. 1996

50 Fluid muds are dense, nearbed suspensions of fine sediments O(10 g/l) or more Characterized by one or more strong density gradients due to suspended sediment, lutoclines Alter the characteristics of the flow

51 Formation? Resuspension by currents? OR Resuspension by waves?

52 Probably not resuspension by waves or currents!

53 Enhanced settling flux, flocculation and hindered settling are key

54 Ross and Mehta, 1989 Winterwerp and van Kesteren 2004

55 Low settling flux High settling flux

56 Fluid muds first observed in estuaries, found to be thick and persistent on Amazon shelf during AMASSEDS ( 89-91) Kineke et al. 1996

57 Region of fluid muds does not coincide with region of turbid surface plume Kineke et al. 1995

58 Foreset Deposits Thanks Geyer and WHOI Graphics

59 ~10g/l Kineke et al. 1996

60 Motivation: Results from AMASSEDS U B > or < 2? ~ SSC ~U U B is integrated buoyancy anomoly B Trowbridge and Kineke 1994 See also Wright, Friedrichs, Kim and Scully 2001 and following papers for application

61 Moncton Petitcodiac River 5nm

62 The Petitcodiac River

63 1 km 2003

64 The Petitcodiac River Strong flows! High concentrations! Fluid muds! Early Flood ~ Slack High

65 Objectives Examine controlling factors in the formation and destruction of fluid mud under a sheared flow Verify critical gradient Richardson number dependence for suppression of turbulence and carrying capacity of a high-concentration suspension Evaluate effects of mixed grain size on the settling of high-concentration suspensions

66 SUBS profiler du, ρ z ( S, T, C), samples dz Instrumentation ctd obs,nozzle em current meters

67 Instrumentation ADV on gafanhoto u'w' Surfboard (ADCP, Knudsen) U z, thickness

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71 Ebb Flood

72 Preliminary* Results AMASSEDS U B < or > 2? U U B B *Caution! Kineke AGU results. Careful Masters students results in progress (Kristy Heath) show more examples below threshold

73 U B < 2

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75 Appendix: Sediment Trapping in Winyah Bay due to Frontogenesis

76 Motivation: Localized areas of high susp. sed. concentration in water column and fine sediment accumulation well downstream of turbidity max WB-8 WB-9 Sediment grab observations rocks & shells sand & shells sand, shells, mud shells sand & mud WB-7 WB-6 WB-5 sand stiff mud soft mud Winyah Bay 70 km N. of Charleston Tides ~ m Discharge: 425 m 3 s -1 2 km WB-4 WB-3 WB-2 WB-1

77 Motivation: Suspended sediment concentrations often uncorrelated with boundary shear stresses

78 Frontogenesis (from Geyer,pers. comm.) Pressure Gradient: p = x g η z ρ z x gρ η x 3 Contributing Factors: Baroclinic Effect Adverse Pressure Gradient Stratification s

79 Conditions Necessary for Frontogenesis 1) Strong, but not too strong, tidal flow 1 Δρ ρ U T gh < 1 2 2

80 Conditions Necessary for Frontogenesis 2) Strong enough expansion for adverse pressure gradient U T / x > 1 ω ω=tidal frequency

81 Conditions Necessary for Frontogenesis 3) Non-trivial baroclinic pressure gradient g ρ h ρ x ωu > 0.2

82 1 U T Δρ gh ρ < (1.3, 1) 7 U T ω / x > 1 (2) 6 g ρ h ρ x ωu > 0.2 (~0.5)

83 Salinity (psu) SSC (g/l) max ebb decel ebb early flood Trapping Length L = uh w f u= 30cm/s h=4m w f =0.1cm/s L=1.2 km

84 7 Observations in 2000 time series floc size Kasten core, 234 Th

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87 ssc mg/l d 50 sal psu w f = mm/s L=0.5 km

88 Sal z< 1m

89 ssc mg/l Sal z<1m d 50 sal psu

90 40 cm deposition w/in 3 months Clark Alexander, SkIO

91 Conclusions Frontogenesis is an efficient and possibly common mechanism for trapping of fine sediments (stratification + front + flocs) Implications for dredging operations are that dredging can enhance sedimentation, but perhaps could be minimized

92 SOME REFERENCES Brown, J., Colling, A., Park, D., Phillips, J., Rothery, D. and Wright, J Waves, Tides and Shallow-Water Processes. Pergamon Press/The Open University, New York, NY, 187 pp. Dyer, K.R Coastal and Estuarine Sediment Dynamics. John Wiley and Sons, New York, 342 pp. Hill, P Controls on Floc Size in the Sea. Oceanography, 11: Kineke, G.C. and Sternberg, R.W Distribution of fluid muds on the Amazon continental shelf. Marine Geology, 125: Kineke, G.C., Sternberg, R.W., Trowbridge, J.H. and Geyer, W.R Fluid-mud processes on the Amazon continental shelf. Continental Shelf Research, 16: MIddleton, G.V. and Southard, J.B Mechanics of Sediment Movement. Society of Economic Paleontologists and Mineralogists. Ross, M.A. and Mehta, A.J On the mechanics of lutoclines and fluid mud. In: High concentration cohesive sediment transport (Eds C.W.J. Finkle, A.J. Mehta and E.J. Hayter), Journal of Coastal Research, pp Coastal Education and Research Foundation (CERF), Fort Lauderdale, FL. Winterwerp, J.C. and van Kestereren, W.G.M Introduction to the Physics of Cohesive Sediment in the Marine Environment. Developments in Sedimentology, 56. Elsevier. Wright, L.D Morphodynamics of Inner Continental Shelves. CRC Press.