1. Entrainment and non-uniform transport of fine-sediment in coarse-bedded rivers Paul E. Grams & Peter R. Wilcock, Johns Hopkins University Stephen M. Wiele, US Geological Survey

2. Acknowledgements USGS – Grand Canyon Monitoring and Research CenterUSGS – Grand Canyon Monitoring and Research Center National Center for Earth-Surface DynamicsNational Center for Earth-Surface Dynamics University of Minnesota – St Anthony Falls LaboratoryUniversity of Minnesota – St Anthony Falls Laboratory

4. Fine sediment transport in rivers with coarse bed material

5. Sand entrainment from a coarse bed: Two aspects of the problem 1.What happens to entrainment as the sand-bed elevation drops?

6. Sand entrainment – coarse bed

10. Sand entrainment from a coarse bed: Two aspects of the problem 1.What happens to entrainment as the sand-bed elevation drops? 2.What is the effect of spatial variability in bed condition?

12. Outline Framework of the entrainment formulation Describe main channel experiments Bed condition and simplified model to represent bed condition Non-uniform routing model Comparison between predicted and observed bed

13. Garcia and Parker (1991) entrainment relation for mixed-size sediment

14. Sand elevation correction function = observed dimensionless entrainment rate = dimensionless entrainment rate for a full sand bed (i.e. Garcia and Parker model) = sand elevation correction function

15. Sand elevation correction function = observed dimensionless entrainment rate = dimensionless entrainment rate for a full sand bed (i.e. Garcia and Parker model) = sand elevation correction function

16. Non-uniform transport to test coupled sand entrainment and sand routing model. Experiments in main channel at SAFL 2.74 x 84 m flume (40 m test section)2.74 x 84 m flume (40 m test section) 60 cm flow depth60 cm flow depth Bed roughness: D = 15 cmBed roughness: D = 15 cm Feed sediment grain size: ~ 0.13 mmFeed sediment grain size: ~ 0.13 mm 5 experimental runs (2-11 hr duration)5 experimental runs (2-11 hr duration)

17. Non-uniform transport to test coupled sand entrainment and sand routing model. Experiments in main channel at SAFL Constant Q: 29 l/sConstant Q: 29 l/s Qs: 2.3 tons/hr for 90 min.Qs: 2.3 tons/hr for 90 min. Initial bed: bare (no fine sediment)Initial bed: bare (no fine sediment) Four segmentsFour segments –1: 90 min. sediment feed –2: 60 min. –3: 145 min. –4: 365 min. 662 min. (11 hr) cumulative run time662 min. (11 hr) cumulative run time

18. Non-uniform transport to test coupled sand entrainment and sand routing model. Experiments in main channel at SAFL Bed topography: measured at the end of each run segment, and sampled for grain sizeBed topography: measured at the end of each run segment, and sampled for grain size Suspended sediment concentration: Three siphon rakes positioned across channel, analyzed for concentration and grain sizeSuspended sediment concentration: Three siphon rakes positioned across channel, analyzed for concentration and grain size

19. 91 min. 152 min. 297 min. 662 min. Main channel bed 40 m 2.7 m

20. Bed of Colorado River in Grand Canyon

21. Bimodal bed – Stripe or Bare stripe bare

22. Distribution of sand bed elevations and sand storage Blue = volume at indicated depthOrange = n for indicated depth

23. Sand elevation correction function from bed morphology “linear relation for the fraction of the bed that is covered by sand stripes based on modal stripe and non- stripe elevations”

24. Sand elevation correction function from bed morphology = Spatially-averaged entrainment rate for a full sand bed = Spatially-averaged sand elevation correction

25. Non-uniform morphodynamic sediment routing model Steady, uniform flow Mixed-size entrainment (Garcia and Parker, 1991) Sand elevation correction function Non-uniform suspended sediment concentration profiles –Velocity and eddy viscosity from measured u profiles Sediment continuity –q T = q s (ignoring transport by bedload) –Active layer ~ bed D50 (fully-mixed) Boundary conditions –Zero flux at water surface –Flux at bed (entrainment rate) –Sediment feed at upstream end

26. Non-uniform morphodynamic sediment routing model Steady, uniform flow Mixed-size entrainment (Garcia and Parker, 1991) Sand elevation correction function Non-uniform suspended sediment concentration profiles –Velocity and eddy viscosity from measured u profiles Sediment continuity –q T = q s (ignoring transport by bedload) –Active layer ~ bed D50 (fully-mixed) Boundary conditions –Zero flux at water surface –Flux at bed (entrainment rate) –Sediment feed at upstream end

27. Non-uniform morphodynamic sediment routing model Steady, uniform flow Mixed-size entrainment (Garcia and Parker, 1991) Sand elevation correction function Non-uniform suspended sediment concentration profiles –Velocity and eddy viscosity from measured u profiles Sediment continuity –q T = q s (ignoring transport by bedload) –Active layer ~ bed D50 (fully-mixed) Boundary conditions –Zero flux at water surface –Flux at bed (entrainment rate) –Sediment feed at upstream end

28. Non-uniform morphodynamic sediment routing model Steady, uniform flow Mixed-size entrainment (Garcia and Parker, 1991) Sand elevation correction function Non-uniform suspended sediment concentration profiles –Velocity and eddy viscosity from measured u profiles Sediment continuity –q T = q s (ignoring transport by bedload) –Active layer ~ bed D50 (fully-mixed) Boundary conditions –Zero flux at water surface –Flux at bed (entrainment rate) –Sediment feed at upstream end

29. Non-uniform morphodynamic sediment routing model Steady, uniform flow Mixed-size entrainment (Garcia and Parker, 1991) Sand elevation correction function Non-uniform suspended sediment concentration profiles –Velocity and eddy viscosity from measured u profiles Sediment continuity –q T = q s (ignoring transport by bedload) –Active layer ~ bed D50 (fully-mixed) Boundary conditions –Zero flux at water surface –Flux at bed (entrainment rate) –Sediment feed at upstream end

31. No SEC

32. SEC from 2002 lab data

33. Theoretical SEC

34. SEC calibrated to main channel bed elevations

35. Comparison between observed and predicted mean bed elevations * all values in meters

36. Concentration profiles Simulated vs. observed

37. Bed grain size (D50) Simulated vs. observed

38. Sand elevation correction function Yes or No? Which to choose? Blue – 2002 data –Bed evacuates too rapidly Orange – theoretical –Decent prediction Yellow – Calibrated –Best fit to observed

39. Sand elevation correction function Yes! Don’t know! Blue – 2002 data –Bed evacuates too rapidly Orange – theoretical –Decent prediction Yellow – Calibrated –Best fit to observed

40. Conclusions In these conditions of fine sediment transport over a coarse immobile bed, sand stripes developed and persisted as the fine sediment was evacuated.In these conditions of fine sediment transport over a coarse immobile bed, sand stripes developed and persisted as the fine sediment was evacuated. This bed condition can serve as the basis for a spatially- averaged sand elevation correction function.This bed condition can serve as the basis for a spatially- averaged sand elevation correction function. This function implemented in a non-uniform routing model successfully predicts average bed elevation, concentration profiles, and bed grain size.This function implemented in a non-uniform routing model successfully predicts average bed elevation, concentration profiles, and bed grain size. Predicted bed elevations are not very sensitive to the exact shape of the correction function. Calibrating the function produces only slightly better results.Predicted bed elevations are not very sensitive to the exact shape of the correction function. Calibrating the function produces only slightly better results.

41. What does the local sand elevation correction function look like? Theoretical approach: Observations from detailed experiments using PIV