Why large rivers have low-angle dunes. Department of Geography. Simon Fraser University. Burnaby, BC, Canada, V5A 1S6. Last revised August 10, 2015

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1 Why large rivers have low-angle dunes Ray Kostaschuk 1* and Jeremy G. Venditti 1 1 River Dynamics Research Group Department of Geography Simon Fraser University Burnaby, BC, Canada, V5A 1S6 Last revised August 10, 2015 DRAFT DO NOT CIRCULATE OR CITE Manuscript in preparation for Nature Geoscience KITP Preprint NSF-KITP [Type text] [Type text] ]

2 Dunes are prominent landforms in rivers, oceans and deserts and play a fundamental role in flow resistance and sediment dynamics. For more than 100 years, characteristic sedimentary structures left behind during downstream dune migration have been used to calculate paleoflow directions and magnitudes in rocks 1. This link between the rock record and modern sedimentary processes is predicated on the principle of scale invariance: the idea that the processes dominating landform development at small scales are the same as at larger scales 2, 3. Small highangle dunes in shallow flows are characterized by steep downstream-facing leefaces ( 30º) with well-developed separation zones of reversed flow 4. Large low-angle dunes in deeper flows have gently sloping leefaces (<25º, often <10º) with predominantly decelerated downstream flow and intermittent reversed flow 5, 6. We propose that dunes are not scale invariant landforms and that they systematically change their morphology as they increase in size because of a transition in leeface sand flow processes. The steep leefaces of high-angle dunes are maintained by grain flows that are initiated by failure of a thin wedge of bedload at the top of the leeface 7,8. The bedload wedge of low angle dunes is thicker and deposited more rapidly, causing excess pore water pressures on failure that produce liquefaction sand flows 9-11 that flow on low leeface gradients. Dune morphology is modified by deposition of sand from suspension in the trough and lower leeface 12,13 and by downstream fluid flow over the leeface 14,15 that increases in importance as leeface angle decreases. 2

3 Bed-material sediment in rivers is transported as bedload (traction and saltation) and in intermittent suspension as suspended bed-material load (hereafter suspended load ). As soon as bed-material transport begins, ripples and dune bedforms develop 3. Dunes can be classified on the basis of streamwise profiles (Fig. 1a) as high-angle and low-angle 4, where angle here refers to that of the lower, straight, downstream-facing leeface. High-angle dunes (HADs) have long, gently-sloping, upstream-facing stoss sides and short, steep downstream-facing leefaces around 30 o with well-developed separation zones of reversed flow and relatively large height/length ratios. In contrast, low-angle dunes (LADs) have stoss and lee sides of similar length, leefaces less than 30º, zones of flow deceleration or intermittent separation rather than permanently reversed flow, and smaller height/length ratios. HADs are small-scale dunes, generally developed in shallow flows (<3 m) or as secondary superimposed dunes on the stoss side of both larger HADs and LADs 16. LADs however are the preeminent dune form in deep rivers (>3 m) with large dunes 5,8, For example, a survey of 1400 dunes in the sand-bed Jamuna River 19 revealed a mean leeface angle of 8.4 o, with less than 3% of the dunes having angles greater than 30 o. Remarkably, HADs continue to serve as the standard dune model 20 because of the ease with which they are produced in the laboratory, despite the overwhelming field evidence that dunes in large rivers are LADs with distinctly different morphologies and dynamics. The key to addressing this dichotomy is a better understanding of leeface processes, particularly the dynamics of mass sand flows on the leeface. We have compiled a data set (see Methods) of dune lee side angles from rivers around the world and from several laboratory experiments (Fig. 1). The data set includes dunes formed in medium sand to fine gravel and span formative flow depths of 0.1 to 24 m. Small dunes in flume experiments and in shallow rivers have leeface angles >25 o, whereas leeface angles of larger 3

4 dunes in the field range between 6 and 21 o Leeface angle is inversely correlated with dune height (Fig. 1b), length (Fig. 1c), height/length (Fig 1d), mean velocity (r s = -0.58, p = ) and flow depth (r s = -0.71, p = ). Leeface angle is thus lower for larger and flatter dunes in faster and deeper flows. A prominent explanation for LADs is deposition from suspension on the leefaces of large dunes 3,5, a hypothesis that we examine using scale models of a HAD and a LAD (Fig. 2a; see Methods). Suspended particle trajectories angle downward from horizontal over the leeside in the lower portion of the flow, reflecting topographic forcing and negative (downward) vertical velocities. Sand transported over the brinkpoint of the HAD is deposited rapidly on the leeface, with less than 25% of the flux bypassing the trough. This result is consistent with recent measurements by over laboratory dunes 21, with bypass fractions of 10-27%. Significant quantities of suspended sediment can also be deposited in the trough of HADs when sediment transport rates increase, although the leeface angle remains steep. For the LAD, only about 10% of the suspended flux is captured on the trough and leeface with 90% bypassing the dune, values comparable to field measurements 22. Recent high-resolution multibeam echosounder images of LADs in the Fraser River 23 show that suspended sand is deposited primarily in the dune trough, with some deposition on the lower leeface. Thus a larger fraction of sand transported in suspension is captured in the trough and leeface of HADs compared to LADs and the portion captured on LADs is deposited on the lower leeface and trough. Deposition from suspension plays a role in LAD morphology, primarily through deposition on the lower leeface and in the trough, but it fails to answer several critical questions on LAD leeface processes: 1. What happens to the bedload that arrives at the brinkpoint 7? It is possible that bedload accumulates at the top of leeface and produces a localized steeply-sloping 4

5 secondary face while most of the leeface is maintained by deposition from suspension, but this process has never been observed. 2. How can LADs persist in bedload dominated rivers where there is little suspended bed-material load? Dunes in the Rhine River 24 are LADs with leefaces of o even though the bed-material is coarse sand and there is little evidence of it in suspension. 3. How can a LAD migrate downstream and maintain a consistent low-angle leeface? The mean deposition rate from suspension over the entire leeface would have to be identical along the profile in order to account for the maintenance of a straight leeface and consistent slope angle as the dune migrates such remarkable fine-tuning is improbable. We believe that liquefaction of bedload that has accumulated at the dune brinkpoint provides answers to these questions. Subaqueous sediment flows are often affected by liquefaction where a framework of loosely packed sand suddenly collapses, generating excess pore pressures and lowering the strength of the sediment mass; liquefied sand flows can flow at angles as low as 1º 12. Observations of HADs in flumes (Fig. 2b, see Methods) have shown that bedload arrives at the brinkpoint either from sheet flow or a secondary bedform 7,25 and accumulates at the top of the leeface as a wedge with a downstream slope at the static angle of repose, up to 38 o for angular sand 8. The failure of the wedge generates a thin, lobate sand flow, or grain flow, that stops on the leeface at a dynamic angle of repose of around 30 o 8 (Fig. 2c). Multibeam echosounder images of large dunes in the field display sand lobes 26 (Fig. 2d) that are similar in shape to those on small HADs, indicating that sand flows occur on low-angle dunes as well. Experiments on Fraser River sand 13 show that liquefaction can produce friction angles of 4-12 o, which are characteristic of leefaces of Fraser dunes. Excess pore pressure increases linearly with flow thickness 11 so the larger and thicker bed load wedges on LADs are more likely to liquefy and flow on gentle gradients. Bedload transport rates will also be higher for LADs because of their larger flow 5

6 velocity and depth 6 so we expect that the sediment deposited in the wedge to have a loose structure and be more susceptible to liquefaction 27. These interpretations are supported by an exposure of a preserved dune in a Late Precambrian fluvial sandstone that shows low-angle foreset beds (10-20 o ), deposits from the leeface of migrating dunes, containing evidence of sand flows, along with deposition from suspension on the lower leeface 28. We believe that the transition from grain flows on HADs to liquefaction flows on LADs is dependent on the size of the dune and is the fundamental scale control on dune morphology. Field measurements in large rivers show that some dunes have steep leefaces at or much greater than 30 o. This is likely due to variation in the three-dimensional shape of dunes. Saddleshaped (concave-downstream) crests generally have greater, but more localized, areas of scour in their lee and steeper leefaces compared to straight-crested or lobe-shaped (convex-downstream) crest lines 16. Enhanced scour in the trough 27 may undermine the base of the leeface, causing slope failures near the static angle of repose or even steeper if dilatancy occurs. Dilative behavior results when the volume of sand expands on failure, resulting in reduced pore pressures internally and maintenance of steep subaqueous slopes 10,11. Flume experiments on fixed dunes 6,29 and field observations in the Missouri River 30 show that flow separation becomes increasingly intermittent and weak as leeface angle decreases below 30 o and disappears at around 10 o 15. This causes an associated increase in strength and duration of downstream fluid flow, and associated bed sediment transport, over the leeface as it becomes fully attached to the bed. High-resolution multibeam echosounder measurements over the 10 o leeface of a LAD 14 found no evidence for time-averaged flow separation and the presence of the small, downstream-oriented, superimposed bedforms on the leeface provides direct evidence for downstream, attached flow and related sediment transport. 6

7 Field observations suggest a very different conceptual model for dunes than the current model based on HADs 20 (Fig. 3), one that undermines the idea of scale invariance in Earth surface dynamics. The leeface (>25 o ) of small dunes (Fig. 3: α = 30 o ) is maintained by failure of a bedload wedge which generates grain flows and creates a flow separation zone with reversed flow. As dune size increases leeface slope decreases because the bedload wedge is thicker and deposited rapidly, resulting in liquefied sand flows that stop on gentler gradients (Fig. 3: α = 20 o ). The flow separation zone is smaller, flow reversal is intermittent and sediment movement by downstream fluid flow over the leeface increases in importance as leeface angle decreases. Flow separation disappears at leeface slopes of 10º (Fig. 3: α = 10 o ) and sediment transport is primarily by downstream fluid flow although liquefaction flow is also possible. Deposition from suspension acts mainly to reduce dune height. Over a century of research on bedforms in laboratories have been undertaken under the assumption that the processes operating at small scales can be translated up to field scale, without consideration of the changes in process domain that may occur. The preeminence of low-angle dunes in large channels suggests that much of what we know about sediment transport dynamics in sand-bedded rivers and how that translates into low-angle dunes preserved in the rock record 28 needs to be rethought. 7

8 References 1. Allen, J.R.L Sedimentary structures: Sorby and the last decade. Journal of the Geological Society, 150, p , doi: /gsjgs Hallet, B. Spatial self-organization in geomorphology: from periodic bedforms and patterned ground to scale-invariant topography. Earth Science Reviews, 29, (1990). 3. Venditti, J.G. Bedforms in sand-bedded rivers. in Treatise on Geomorphology, (eds Shroder. J. & Wohl, E.) Vol. 9 Fluvial Geomorphology , (Academic Press, 2013). 4. Bennett, S.J. & Best, J.L. Mean flow and turbulence structure over fixed, twodimensional dunes: implications for sediment transport and bedform stability. Sedimentology, 42, (1995). 5. Best, J. & Kostaschuk, R. An experimental study of turbulent flow over a low- angle dune. Journal of Geophysical Research Oceans, 107(C9), doi: / 2000JC (2002). 6. Bradley, R. W., Venditti J.G., Kostaschuk, R.A., Church, M., Hendershot, M. L. & Allison M.A. Flow and sediment suspension events over low-angle dunes: Fraser Estuary, Canada. Journal of Geophysical Research Earth Surface, 118, , doi: /jgrf (2013). 7. Kleinhans, M.G. Sorting in grain flows at the lee side of dunes. Earth Science Reviews 65, (2004). 8

9 8. Lunt, I.A. & Bridge, J.S. Formation and preservation of open-framework gravel strata in unidirectional flows. Sedimentology, 54, doi: /j x (2007). 9. Pailha, M. & Pouliquen, O. A two-phase flow description of the initiation of underwater granular avalanches. Journal of Fluid Mechanics, 633, (2009). 10. Rao, A., Chillarige, V., Robertson, P.K., Morgenstern, N.R. & Christian, H.A. Evaluation of the in situ state of Fraser River sand. Canadian Geotechnical Journal, 34, (1997). 11. Vaid, Y.P. & Sivathayalan, S. Fundamental factors affecting liquefaction susceptibility of sands. Canadian Geotechnical Journal, 37, (2000). 12. Kostaschuk, R.A., Sediment transport mechanics and dune morphology, in River, Coastal and Estuarine Morphodynamics: RCEM 2005 (eds Parker G. & Garcia M.) (Taylor & Francis, 2005). 13. Kostaschuk, R.A. & Villard, P.V. Flow and sediment transport over large subaqueous dunes: Fraser River, Canada. Sedimentology, 43, (1996). 14. Best, J., Simmons, S., Parsons, D, Oberg, K., Czuba, J. & Malzone, C. A new methodology for the quantitative visualization of coherent flow structures in alluvial channels using multibeam echo-sounding (MBES). Geophysical Research Letters, 37, L06405, doi: /2009gl (2010). 15. Lefebvre, A. Paarlberg A.J., Ernstsen V.B. & Winter, C. Flow separation and roughness lengths over large bedforms in a tidal environment: A numerical investigation. Continental Shelf Research, 91, (2014). 9

10 16. Parsons, D. R., Best, J. L., Orfeo, O, Hardy, R. J., Kostaschuk, R.A. & Lane, S.N. Morphology and flow fields of three-dimensional dunes, Rio Parana, Argentina: Results from simultaneous multibeam echo sounding and acoustic Doppler current profiling. Journal of Geophysical Research Earth Surface, 110, F04S03, doi: /2004jf (2005). 17. Smith, J. D. & McLean S. R. Spatially averaged flow over a wavy boundary. Journal of Geophysical Research Oceans, 82, (1977). 18. Nittrouer, J. A., Allison, M. A. & Campanella, R. Bedform transport rates for the lowermost Mississippi River. Journal of Geophysical Research Earth Surface, 113, F03004, doi: /2007jf (2008). 19. Roden, J.E. The sedimentology and dynamics of mega-dunes, Jamuna River, Bangladesh. PhD thesis, Department of Earth Sciences and School of Geography, University of Leeds, Leeds, U.K. (1998). 20. Coleman, S.E. & Nikora, V.I. Fluvial dunes: initiation, characterization, flow structure. Earth Surface Processes and Landforms, 36, (2011). 21. Naqshband, S., J. Ribberink, S., Hurther, D. and Hulscher, S. J. M. H. Bed load and suspended load contributions to migrating sand dunes in equilibrium, Journal of Geophysical Research Earth Surface, 119, , doi: /2013jf (2014). 22. Kostaschuk, R, Shugar, D., Best, J., Parsons, D., Lane, S., Hardy, R. & Orfeo, O. Suspended sediment transport and deposition over a dune: Río Paraná, Argentina. Earth Surface Processes and Landforms, 34, (2009). 10

11 23. Hendershot, M.L., Venditti, J.G., Bradley, R., Kostaschuk, R.A. Church, M.A. & Allison, M.A. Response of low-angle dunes to variable flow. Sedimentology (in press). 24. Wilbers, A.W.E. & Ten Brinke W.B.M. The response of subaqueous dunes to floods in sand and gravel bed reaches of the Dutch Rhine. Sedimentology, doi: /j x (2003). 25. Venditti, J. G., Church, M. & Bennett, S.J. Morphodynamics of small-scale superimposed sand waves over migrating dune bed forms, Water Resources Research, 41, W10423, doi: /2004wr (2005). 26. Poppe, L.J., Ackerman, S.D., Foster, D.S., Blackwood, D.S., Williams, S.J., Moser, M.S., Stewart, H.F. & Glomb, K. A. Sea-floor character and sedimentary processes of Great Round Shoal Channel, offshore Massachusetts. U.S. Geological Survey Open-File Report (2007). 27. di Prisco, C., Mancinelli, L., Zanelotti, L. and Pisanò, F. Numerical stability analysis of submerged slopes subject to rapid sedimentation processes. Continuum Mechanics and Thermodynamics, 27, DOI /s y (2015). 28. Røe, S.L. Cross-strata and bedforms of probable transitional dune to upper-stage planebed origin from a Late Precambrian fluvial sandstone, northern Norway, Sedimentology, 34, (1987). 29. Kwoll, E. Bedforms, macroturbulence and sediment transport at the fluid-bed interface. PhD Thesis, Centre for Marine and Environmental Sciences, University of Bremen, Bremen, Germany. 30. Holmes, R.R. & Garcia, M.H. Flow over bedforms in a large sand-bed river: A field investigation. Journal of Hydraulic Research, 46, (2008). 11

12 Acknowledgements: This work was inspired by RK s participation in the Program Fluid-mediated Particle Transport in Geophysical Flows held in 2013 at the Kavli Institute for Theoretical Physics (KITP), University of California Santa Barbara. This research was supported in part by the National Science Foundation under Grant No. PHY Funding was also provided by Natural Sciences and Engineering Research Council of Canada Discovery Grants to RK and JV. 12

13 Figures Figure 1. (a) Definition diagram for streamwise dune profile morphology, where α is the leeface slope angle and FSZ is the flow separation zone. (b-d) Empirical plots for dune morphology, where r s is the non-parametric Spearman correlation coefficient and p is the probability that the result occurred by chance (see Methods). 13

14 Figure 2. (a) Suspended particle trajectories over the scale models of a high-angle dune (HAD) 4 and a low-angle-dune (LAD) 5 (see Methods). Trajectories are based on measurements of horizontal and vertical fluid velocity from the original experiments, with particle settling velocity added to the vertical velocity at each point. G 10 G 25, and G 50 are the 10 th 25 th, and 50 th percentiles of unit sediment flux at the brinkpoint respectively (see Methods). (b) Initiation of bedload sand flows from a sediment wedge on the upper leeface (based on flume observations 7, see Methods), where 1 is time 1, 2 is time 2, α s is the static angle of repose, α d is the dynamic angle of repose and α is the leeface slope angle. (c) Leeface sand flows on a high-angle dune in a flume at Simon Fraser University (see Methods and Supplementary Video 1). (d) Multibeam echosounding map of LADs in the Fraser River, British Columbia. The red arrows indicate the direction of sediment transport in sand lobes and the blue arrow indicates the mean river flow direction. 14

15 Figure 3. Two-dimensional conceptual model for flow and sediment transport pathways over dunes. The panels show the interaction between leeface angle α and flow and sediment dynamics (see text for explanation). FSZ refers to the flow separation zone and velocity vectors are based on scale model experiments 4,5. The thickness of the sediment transport arrows indicates their relative importance. 15

16 Methods Dune Data Compilation. Although there have been numerous flume and field studies of bedform morphology, few provide the detailed data on flow and sediment characteristics required for this investigation. The data used in this study are summarized in Extended data Table 1, which are all reach-averaged to reduce variability within the dune field. The relation between dune length (L) and height (H) for the data of Table 1 (Extended Data Fig. 1) is a highly significant power function with an exponent that indicates that the dunes have a flatter profile as they increase in length. This relation is nearly identical to an empirical relation 31 based on around 1500 measurements of bedforms in flumes, rivers, tidally influenced rivers, and marine environments. The similarity of these empirical functions and the strength of the relation between H and L indicate that the data of Table 1 are representative of bedforms in the worlds rivers and provide a useful basis for subsequent empirical analysis. Scale modeling. We use fixed-bed flume experiments 5,6 to examine the detailed flow dynamics and suspended sand trajectories over HADs and LADs. The experiments used the same flume and laser Doppler anemometer for detailed measurements of the streamwise and vertical components of fluid velocity over a single dune. The LAD experiment 6 was based on field data 13 using Froude-scaling (Fr = 0.15) for flow over a 1:58 scale dune. Because mean streamwise velocity (0.22 ms -1 ) and depth (0.2 m) in the LAD experiment were much lower than those in the field (1.61 ms -1 and 11.5 m respectively) it is not possible to examine sediment dynamics in a manner that would be comparable to those over the HAD. In particular, we would be unable to compute the trajectories of suspended particles using the scale model. As a result, we rescaled 16

17 the flume results back to the field scale such that dune geometry, mean streamwise velocity and depth matched those of the field dune. This approach has the advantage of providing substantially more velocity data than the original field measurements and velocity measurements that are much closer to the bed. The mechanics of suspended bed-material transport and deposition on dune leesides were examined by plotting the trajectories of sediment particles beyond the brinkpoint. Trajectories were determined for the median particle size of bed sediment, which was 0.3 mm in both cases. The settling velocity of the particles (0.04 ms -1 ) was added to the measured fluid velocity over the dune leeside and particle vectors calculated in conjunction with horizontal fluid velocity. We used a suspended sediment model 32 (Extended data Fig. 2) to compute the concentration profile of bed-material above the brinkpoint. Suspended load was determined as the product of concentration and fluid velocity. Sand flows. Sand flows on HADs were examined using video of migrating dunes (Supplementary Video 1) in a 1 m wide sand bed flume at Simon Fraser University. Highresolution multibeam echosounder images were used to identify bed load wedges on LADs in the Parana River (Extended data Fig. 3) and to identify sand flows on LADs in the Fraser River

18 Extended data Table 1. Reach/study averaged dune, flow and sediment characteristics. H is dune height, L is dune length, α is leeface angle, U is mean flow velocity, h is mean flow depth, D 50 is median bed-material grain size, adcp is acoustic Doppler current profiler and MBES is multibeam echosounder. Source H (m) L (m) α ( o ) U (m/s) h (m) D 50 (mm) Flume Flume 33 Exp T Flume Flume 35 Exp Calamus River 36 April , 1125 h; Fraser River 37 low tide, June Fraser River 6 low tide Green River Jamuna River 19 September Lillooet River 39 August , 1535 h Missouri River 29 MO Ob River: May 2010; (unpublished adcp data) Rhine River 40 dune 94/ Rhine River 41 Bovenrijn section 1: Feb Rio Paraná, Paso de la Patria: May 2004 (unpublished adcp and MBES data) Rio Paraná, Paso de la Patria: March 2004 (unpublished adcp and MBES data Rio Paraná, Santa Fe: May 2004; (unpublished adcp and MBES data)

19 Figure 1. (a) Empirical relation for dune length and height for the data of Table 1. R 2 is the coefficient of determination. 19

20 Figure 2. Non-dimensional suspended sediment and velocity profiles above the brinkpoint for the (a) high-angle dune (HAD) and (b) low-angle dune (LAD) of Fig. 2a. y is height above the brinkpoint, h b is the depth at the brinkpoint, C is bed material concentration, C a is concentration at y/h b = 0.01, G is bed-material flux, G max is the maximum flux in the profile, U is streamwise velocity, U max is the maximum velocity in the profile. 20

21 Figure 3. Bed load wedge caused by a migrating, superimposed HAD on a LAD in the Parana River, Argentina. (a) shaded relief multibeam echosounder image, with the red line indicating the location of the transect on (b). The blue arrow indicates the mean flow direction. 21

22 References for Methods and Extended Data 31. Flemming, B.W. Zur klassifikation subaquatistischer, stromungstrans versaler transportkorper. Bochumer Geologische und Geotechnisce Arbeiten, 29, (1988) 32. van Rijn, L.C. Sediment transport, Part 11: suspended load. Journal of Hydraulic Engineering, 110, (1984). 33. Blom, A., Ribberink, J. S. & de Vriend, H. J. Vertical sorting in bed forms: Flume experiments with a natural and a trimodal sediment mixture, Water Resources Research, 39(2), 1025, doi: /2001wr (2003). 34. Robert, A. & Uhlman, W. An experimental study on the ripple-dune transition. Earth Surface Processes and Landforms, 26, (2001). 35. Tuijnder, A.P., Ribberink, J.S. & Hulscher, S.J.M.H. An experimental study into the geometry of supply-limited dunes. Sedimentology, 56, (2009). 36. Gabel, S.L. Geometry and kinematics of dunes during stready and unsteady flows in the Calamus River, Nebraska, USA. Sedimentology, 40, (1993) 37. Kostaschuk, R.A. & Ilersich, S.A. Dune geometry and sediment transport. in River Geomorphology, (ed Hickin, E.J.) (John Wiley & Sons,1995) 38. Venditti, J.G. & Bauer, B.O. Turbulent flow over a dune: Green River, Colorado. Earth Surface Processes and Landforms, 30, (2005) 39. Prent, M.T.H. & Hickin, E.J. Annual regime of bedforms, roughness and flow resistance, Lillooet River, British Columbia, BC. Geomorphology, 41, (2001). 22

23 40. Carling, P.A., Gölz, E., Orr, H.G. & Radecki-Pawlik, A. The morphodynamics of fluvial sand dunes in the River Rhine, near Mainz, Germany. I. Sedimentology and morphology. Sedimentology, 47, (2000). 41. Wilbers, A.W.E. Prediction of bedform characteristics and bedform roughness in large rivers. Unpublished Ph D thesis, Utrecht University (2004). 23