1. Basic sediment transport
Initial motion & bedload
Definitions and dimensions
Shields stress and initial motion
Bedload formulas
Shear stress
Stress & flow
Measurement & estimation
Suspension, wash load, total load
Rouse number & profile
Total-load formulas
Links between topography and sediment flux

2. Sediment characterization
Wentworth scale

3. Grain size distribution
Unimodal sand

4. To the board! analysis of initial motion: forces, force balance
dimensional analysis and Shields stress
rough analysis of critical Shields

5. Shields initial motion
From Buffington (1999)

6. Shields initial motion

7. Initial motion: standard conditions
No motion
Peter Wilcock, Utah State Univ.

8. Modifying Shields for slope effects
Streamwise slope
Lateral slope

9. What to do about size mixtures?
When grain sizes are clearly segregated into patches like this, you can apply Shields to each patch separately.

10. Within a mixture, all sizes tend to move together up to very large clasts
mixture effects diminish for extremely large grain sizes
Di / D50
Parker; Wilcock; Proffitt & Sutherland

11. Initial motion -- summary
Brownlie formula for Shields curve:
Correction for streamwise slope:
Correction for side slope:
Correction for mixtures:
NB Parker et al. (2003) have suggested reducing this by a factor of 2

12. Bedload + Suspended load = Total load

13. Bedload – Meyer-Peter & Müller
KMPM = 8 in the original formulation; corrected to 4 by Wong & Parker (2005)

14. Bedload – more relations
threshold
Ashida - Michue
no threshold
Einstein
Parker mod. to Einstein

15. Parker 1990 gravel
appropriate for gravel bedload transport rates in gravel-bed streams
Fi must be renormalized so that the sand is removed, and the remaining gravel fractions sum to unity, Fi = 1.
based on surface geometric size Dsg and surface arithmetic standard deviation s on the  scale, both computed from the renormalized fractions Fi.

16. Bedload vs suspension suspension Fw ~ w’ (turbulence) bedload
Fw ~ bed (collisions, contact)

17. Bedload vs suspension Turbulent fluctuations w’ ~ u
suspension if u ~ settling vel ws
Rouse number Ro

18. Bedload vs suspension

19. Bedforms

20. Bedform types: unidirectional flow
ripples

21. Bedform types: unidirectional flow
dunes

22. Bedform types: unidirectional flow
dunes

23. Bedform types: unidirectional flow
Kennetcook River, NS
Wolfville FM, Red Head, NS
dunes

24. Bedform types: unidirectional flow
plane bed

25. Bedform types: unidirectional flow
antidunes

26. Bedform stability Southard (1991) 0.2 0.4 0.6 0.8 1.0 2.0
Southard (1991)

27. Bedform stability Southard (1991) 0.2 0.4 0.6 0.8 1.0 2.0
Southard (1991)

28. Bedform stability Southard (1991) 0.2 0.4 0.6 0.8 1.0 2.0
Southard (1991)

29. Bedform stability For flow depths: Southard (1991)
Southard (1991)

30. Bedform stability
Southard (1991)

31. Bedforms - summary Ripples D < 0.5 mm  < 0.3 m /hbf ~15
u ~ uc
Upper plane bed
D = any
u > ws
Dunes
D > 0.2 mm
hbf ~ 0.3 h
/hbf >15
ws> u >> uc
Antidunes
D = any
Fr = U/gh ~ 1

32. Bed forms and form drag
Herrmann et al., 2005, Physica A

33. Can you explain this?
Pigeon Roost Creek, Mississippi

34. Bedload + Suspended load = Total load

35. Suspension  total load
The Rouse theory for suspension is well developed and compares well with data
BUT it depends on a lower boundary condition that is set by bedload
Since bedload flux is determined empirically, in the end so is suspended flux and hence total load
suspended flux per unit width

36. Total load formulas Engelund-Hansen (1967) Brownlie (1981)
K = 1 for lab data
= for field data
r = hydraulic radius (Area/wetted perimeter

37. Brownlie grand comparison

38. Van Rijn (1984)
An attempt to synthesize the “best of” sediment transport (mainly sand) over many years
VR(a): bedload
VR(b): suspended load
VR(c): bedforms & roughness

39. Van Rijn (1984)
Van Rijn, L. C. (1984a), Sediment transport, part I: bed load transport, Journal of Hydraulic Engineering, 110(10),
Van Rijn, L. C. (1984b), Sediment transport, part II: suspended load transport, Journal of Hydraulic Engineering, 110(11),
Van Rijn, L. C. (1984c), Sediment transport, part III: bed forms and alluvial roughness, Journal of Hydraulic Engineering, 110(12),