Skip to main content
Log in

Hydraulic roughness over simple subaqueous dunes

  • Original
  • Published:
Geo-Marine Letters Aims and scope Submit manuscript

Abstract

Detailed studies of flow over subaqueous dunes in laboratory flumes were used to suggest a virtual near-bed layer of twice the dune height in which the mean velocity is accelerated towards the crest by contraction. The mean flow velocity in this layer above the crest, transformed into friction velocity by means of the surface skin roughness, is shown to give values consistent with measured values. The resulting dimensionless shear stress due to skin friction is depth-independent, in contrast to that derived by means of often cited traditional methods. As a result of the relationship between dune height and the thickness of the near-bed layer, an expression for the expansion loss behind dunes was formulated and used to relate form resistance directly to dune height.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Ashley GM (1990) Classification of large-scale subaqueous bedforms: a new look at an old problem. J Sediment Petrol 60:160–172

    Google Scholar 

  • Bartholdy J, Bartholomae A, Flemming BW (2002) Grain-size control of large compound flow-transverse bedforms in a tidal inlet of the Danish Wadden Sea. Mar Geol 188:391–413

    Article  Google Scholar 

  • Bartholdy J, Flemming BW, Bartholom ä A, Ernstsen VB (2005) Flow and grain size control of depth-independent simple subaqueous dunes. J Geophys Research 110:F04S16. doi:10.1029/2004JF000183

    Article  Google Scholar 

  • Bartholdy J, Flemming BW, Ernstsen VB, Winter C, Bartholom ä A (2009) A simple bedform migration model. Earth Surface Processes Landforms (in press)

  • Bartholom ä A, Ernstsen VB, Flemming BW, Bartholdy J (2004) Bedform dynamics and net sediment transport paths over a flood-ebb tidal cycle in the Gr ådyb channel (Denmark), determined by high-resolution multibeam echosounding. Danish J Geogr 104(1):45–55

    Google Scholar 

  • Bennett SJ, Best JL (1995) Mean flow and turbulence structure over fixed, two-dimensional dunes: implications for sediment transport and bedform stability. Sedimentology 42:491–513

    Article  Google Scholar 

  • Carling PA (2000) The morphodynamics of fluvial sand dunes in the River Rhine, near Mainz. Germany. II. Hydrodynamics and sediment transport. Sedimentology 47:253–278

    Article  Google Scholar 

  • Einstein HA (1950) The bed-load function for sediment transport in open channel flows. US Department of Agriculture, Tech Bull 1026

    Google Scholar 

  • Einstein HA, Barbarossa NL (1952) River channel roughness. ASCE Trans 117:1121–1146

    Google Scholar 

  • Engelund FA (1964) Flow resistance and hydraulic radius. Acta Polytechnia Scandinavia Civil Engineering and Building Constructions Series no 24, pp 1–23

  • Engelund FA (1966) Hydraulic resistance of alluvial streams. J Hydraul Div ASCE 92:315–326

    Google Scholar 

  • Engelund FA, Freds øe J (1982) Sediment ripples and dunes. Annu Rev Fluid Mech 14:13–37

    Article  Google Scholar 

  • Engelund FA, Hansen E (1967) A monograph on sediment transport in alluvial streams. Teknisk Forlag, Copenhagen

    Google Scholar 

  • Engelund FA, Pedersen FB (1974) Hydraulik. Den Private Ingeni ørfond, Danmarks tekniske H øjskole

    Google Scholar 

  • Ernstsen VB, Noormets R, Winter C, Hebbeln D, Bartholom ä A, Flemming BW, Bartholdy J (2005) Development of subaqueous barchanoid-shaped dunes due to lateral grain size variability in a tidal inlet channel of the Danish Wadden Sea. J Geophys Res Part F Earth Surface 110:F04S08. doi:10.1029/2004JF000180

    Article  Google Scholar 

  • Flemming BW (1978) Underwater sand dunes along the southeast African continental margin — observations and implications. Mar Geol 26:177–198

    Article  Google Scholar 

  • Flemming BW (1988) Zur Klassifikation subaquatischer, str ömungstransversaler Transportk örper. Bochumer Geol Geotech Arb 29:93–97

    Google Scholar 

  • Flemming BW (2000) The role of grain size, water depth and flow velocity as scaling factors controlling the size of subaqueous dunes. In: Trentesaux A, Garlan T (eds) Proc Worksh Marine Sandwave Dynamics, 23–24 March 2000. University of Lille, France, pp 55–60

    Google Scholar 

  • Freds øe J (1982) Shape and dimensions of stationary dunes in rivers. J Hydraul Div ASCE 108:932–947

    Google Scholar 

  • Freds øe J, Deigaard R (1992) Mechanics of coastal sediment transport. World Scientific, London

    Book  Google Scholar 

  • Guy HP, Simons DB, Richardson EV (1966) Summary of alluvial channel data from flume experiments, 1956–61. US Geol Surv Prof Pap 462–I

  • Jackson RG (1976) Sedimentological and fluid-dynamic implications of turbulent bursting phenomena in geophysical flow. J Fluid Mech 77:531–560

    Article  Google Scholar 

  • Kostaschuk RA, Church MA (1993) Macroturbulence generated by dunes: Fraser River, Canada. Sed Geol 85:25–37

    Article  Google Scholar 

  • Kuijpers A, Hansen B, H ühnerbach V, Larsen B, Nielsen T, Werner F (2002) Norwegian Sea overflow through the Faroe-Shetland gateway as documented by its bedforms. Mar Geol 188:147–164

    Article  Google Scholar 

  • McLean SR (1990) The stability of ripples and dunes. Earth-Sci Rev 29:131–144

    Google Scholar 

  • McLean SR, Smith JD (1986) A model for flow over two-dimensional bed forms. J Hydraul Eng 112:300–317

    Article  Google Scholar 

  • McLean SR, Nelson JM, Wolfe SR (1994) Turbulence structure over two-dimensional bed forms: implications for sediment transport. J Geophys Res 99:12729–12747

    Article  Google Scholar 

  • McLean SR, Nelson JM, Shreve RL (1996) Flow-sediment interactions in separating flows over bedforms. In: Ashworth PJ, Bennett SJ, Best JL, McLelland SJ (eds) Coherent flow structures in open channels. Wiley, New York, pp 203–226

    Google Scholar 

  • McLean SR, Wolfe SR, Nelson JM (1999a) Spatially averaged flow over a wavy boundary revisited. J Geophys Res 104:15743–15753

    Article  Google Scholar 

  • McLean SR, Wolfe SR, Nelson JM (1999b) Predicting boundary layer shear stress and sediment transport over bed forms. J Hydraul Eng 125(7):725–736

    Article  Google Scholar 

  • Meyer-Peter E, M üller R (1948) Formulas for bed-load transport. In: Proc 2nd Meet International Association for Hydraulic Structure Research, Stockholm, 7–9 VI, pp 39–63

  • Middleton GV, Southard JB (1978) Mechanics of sediment movement. SEPM, Tulsa, OK, Short Course no 3

    Google Scholar 

  • M üller A, Gyr A (1982) Visualization of the mixing layer behind dunes. In: Sumer M, M üller A (eds) Mechanics of sediment transport. Balkema, Rotterdam, pp 41–45

    Google Scholar 

  • Nikuradse J (1933) Str ömungsgesetze in rauhen Rohren. Forschungs-Arb Ing-Wesen no 361, Berlin

  • Raudkivi AJ (1966) Bed forms in alluvial channels. J Fluid Mech 26:507–514

    Article  Google Scholar 

  • RDI (1996) Acoustic Doppler Current Profiler, Principles of Operation. A Practical Primer, RD Instruments, San Diego, CA

    Google Scholar 

  • Rouse H (1950) Engineering hydraulics. Wiley, New York

    Google Scholar 

  • Schindler JR, Robert A (2005) Flow and turbulence structure across the ripple-dune transition: an experiment under mobile bed conditions. Sedimentology 52:627–649

    Article  Google Scholar 

  • Smith JD, McLean SR (1977) Spatially averaged flow over a wavy surface. J Geophys Res 12:1735–1746

    Article  Google Scholar 

  • Sukhodolov AN, Fedele JJ, Rhoads BL (2006) Structure of flow over alluvial bedforms: an experiment on linking field and laboratory methods. Earth Surface Processes Landforms 31:1292–1310

    Article  Google Scholar 

  • Svenson C, Ernstsen VB, Winter C, Hebbeln D (2009) Tide-driven sediment variations on a large compound dune in the Jade tidal inlet channel, Southeastern North Sea. J Coastal Res SI 56 (in press)

  • Tjerry S, Freds øe J (2005) Calculation of dune morphology. J Geophys Res 110:F04013. doi:10.1029/2004JF000171

    Article  Google Scholar 

  • van Rijn LC (1984a) Sediment transport, Part I: Bed load transport. J Hydraul Eng 110(10):1431–1456

    Article  Google Scholar 

  • van Rijn LC (1984b) Sediment transport, Part III: Bed forms and alluvial roughness. J Hydraul Eng 110(12):1733–1754

    Article  Google Scholar 

  • van Rijn LC (1993) Principles of sediment transport in rivers, estuaries and coastal seas. AQUA Publications, Blokzijl, The Netherlands

    Google Scholar 

  • White WR, Paris E, Bettess R (1980) The frictional characteristics of alluvial streams: a new approach. Proc Inst Civil Eng Part 2:737–750

    Article  Google Scholar 

  • Wilson KC (1988) Frictional behaviour of sheet flow. Institute of Hydrodynamics and Hydraulic Engineering, Technical University of Denmark, Prog Rep 67

  • Wilson KC (1989) Mobile-bed friction at high shear stress. J Hydraulic Eng ASCE 115 no 6

    Google Scholar 

  • Wilson KC, Nnadi FN (1990) Behaviour of mobile beds at high shear stress. In: Proc 22nd Coastal Engineering Conf, 1990, Delft. ASCE, New York, vol 3, chap 192, pp 2536–2541

  • Yalin MS (1977) Mechanics of sediment transport, 2nd edn. Pergamon Press, Oxford

    Google Scholar 

  • Yalin MS (1992) River mechanics. Pergamon Press, Oxford

    Google Scholar 

  • Yalin MS, Karahan E (1979) Inception of sediment transport. J Hydraul Div ASCE 105:1433–1443

    Google Scholar 

  • Yang S-Q, Tan S-K, Lim S-Y (2005) Flow resistance and bed form geometry in a wide alluvial channel. Water Resources Res 41:W09419. doi:10.1029/2005WR004211

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jesper Bartholdy.

Electronic supplementary material

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bartholdy, J., Flemming, B.W., Ernstsen, V.B. et al. Hydraulic roughness over simple subaqueous dunes. Geo-Mar Lett 30, 63–76 (2010). https://doi.org/10.1007/s00367-009-0153-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00367-009-0153-7

Keywords

Navigation