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Bedforms

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Fluvial Hydrodynamics

Part of the book series: GeoPlanet: Earth and Planetary Sciences ((GEPS))

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Abstract

Natural streambed does not exhibit a flat bed surface but takes various geometrical forms known as bedforms. In this chapter, the experimental and theoretical studies dealing with the formation, geometry, and stability of bedforms are furnished. The predictors of various bedforms are discussed in details. Bedforms in gravel-bed streams are given. The important feature of this chapter is the presentation of mathematical models proposed by various researchers. Further, the resistance to flow due to bedforms is of paramount importance to river engineers. This issue is also discussed. Numerical examples on bedforms are given in the end of the chapter.

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Notes

  1. 1.

    In terms of Shields parameter, ripples can occur at about Θ = 10–14Θc, where Θ and Θc are the Shields parameter and the threshold Shields parameter, respectively. The Shields parameter is defined as Θ = τ 0/(Δρgd), and the threshold Shields parameter Θc corresponds to the threshold bed shear stress τ 0c. Here, τ 0 is the bed shear stress \( ( = \rho u_{*}^{2} ) \), Δ is the submerged relative density (= s − 1), s is the relative density of sediment (= ρ s/ρ), ρ s is the mass density of sediment, ρ is the mass density of water, g is the acceleration due to gravity, and d is the median particle size.

  2. 2.

    The Kelvin–Helmholtz instability may occur when there is shear at the interface between two flowing fluids.

  3. 3.

    Biunivocal is a type of relationship that exclusively links two terms to one another on the basis of one of the two terms.

References

  • Allen JRL (1968) Current ripples: their relation to patterns of water and sediment motion. North-Holland Publishing Company, Amsterdam

    Google Scholar 

  • Allen JRL (1978) Computational methods for dune time-lag: calculations using Stein’s rule for dune height. Sediment Geol 20(3):165–216

    Article  Google Scholar 

  • Ashley GM (1990) Classification of large scale subaqueous bed forms: a new look at an old problem. J Sediment Petrol 60(1):160–172

    Article  Google Scholar 

  • Athaullah M (1968) Prediction of bed forms in erodible channels. PhD thesis, Department of Civil Engineering, Colorado State University, Fort Collins, Colorado

    Google Scholar 

  • Baas JH (1993) Dimensional analysis of current ripples in recent and ancient depositional environments. Geological Ultraiectina 106, Department of Geology, University of Utrecht, Utrecht

    Google Scholar 

  • Baas JH (1994) A flume study on the development and equilibrium morphology of current ripples in very fine sand. Sedimentology 41(2):185–209

    Article  Google Scholar 

  • Baas JH (1999) An empirical model for the development and the equilibrium morphology of current ripples in fine sand. Sedimentology 46(1):123–138

    Article  Google Scholar 

  • Baas JH, de Koning H (1995) Washed-out ripples: their equilibrium dimensions, migration rate, and relation to suspended-sediment concentration in very fine sand. J Sediment Res A 65(2):431–435

    Google Scholar 

  • Bagnold RA (1946) Motion of waves in shallow water. Interaction between waves and sand bottoms. Proc R Soc London A 187(1008):1–18

    Google Scholar 

  • Bagnold RA (1956) The flow of cohesionless grains in fluids. Philos Trans R Soc London A 249(964):315–319

    Article  Google Scholar 

  • Banks NL, Collinson JD (1975) The size and shape of small-scale current ripples: an experimental study using medium sand. Sedimentology 22(4):583–599

    Article  Google Scholar 

  • Barton JR, Lin PN (1955) A study of sediment transport in alluvial channels. Report number 55JRB2, Department of Civil Engineering, Colorado A and M College, Fort Collins, Colorado

    Google Scholar 

  • Bathurst JC (1993) Flow resistance through the channel network. In: Beven K, Kirkby MJ (eds) Channel network hydrology. Wiley, Chichester, pp 43–68

    Google Scholar 

  • Bechteler W, Vogel G, Vollmers HJ (1991) Model investigations on the sediment transport of a lower alpine river. In: Armanini A, di Silvio G (eds) Fluvial hydraulics of mountain regions. Lecture note in earth sciences. Springer, Berlin, pp 769–857

    Google Scholar 

  • Billi P (1988) A note on cluster bedform behaviour in a gravel-bed river. Catena 15(5):473–481

    Article  Google Scholar 

  • Bose SK, Dey S (2009) Reynolds averaged theory of turbulent shear flow over undulating beds and formation of sand waves. Phys Rev E 80:036304

    Article  Google Scholar 

  • Bose SK, Dey S (2012) Instability theory of sand-ripples formed by turbulent shear flows. J Hydraul Eng 138(8):752–756

    Article  Google Scholar 

  • Brayshaw AC, Frostick LE, Reid I (1983) The hydrodynamics of particle clusters and sediment entrainment in coarse alluvial channels. Sedimentology 30(1):137–143

    Article  Google Scholar 

  • Brooks NH (1954) Laboratory studies of the mechanics of streams flowing over a movable bed of fine sand. Doctoral thesis, California Institute of Technology, Pasadena

    Google Scholar 

  • Brownlie WR (1983) Flow depth in sand-bed channels. J Hydraul Eng 109(7):959–990

    Article  Google Scholar 

  • Chabert J, Chauvin JL (1963) Formation de dunes et des rides dans les modèles fluviaux. Bulletin du Centre de Recherches et d’essais de Chatou 4:31–51

    Google Scholar 

  • Cheng N-S (1997) Simplified settling velocity formula for sediment particle. J Hydraul Eng 123(2):149–152

    Article  Google Scholar 

  • Chin A (1999) The morphologic structure of step-pools in mountain streams. Geomorphology 27(3–4):191–204

    Article  Google Scholar 

  • Colebrook CF, White CM (1937) Experiments with fluid friction in roughened pipes. Proc R Soc London A 161(906):367–381

    Google Scholar 

  • Davies TR (1971) Summary of experimental data for flume tests over fine sand. Report CE/3/71, Department of Civil Engineering, University of Southampton, Southampton

    Google Scholar 

  • Einstein HA, Barbarossa NL (1952) River channel roughness. Trans Am Soc Civ Eng 117:1121–1132

    Google Scholar 

  • Engelund F (1966) Hydraulic resistance of alluvial streams. J Hydraul Div 92(2):315–326

    Google Scholar 

  • Engelund F (1970) Instability of erodible beds. J Fluid Mech 42:225–244

    Article  Google Scholar 

  • Engelund F, Fredsøe J (1982) Sediment ripples and dunes. Ann Rev Fluid Mech 14:13–37

    Article  Google Scholar 

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

    Google Scholar 

  • Exner FM (1925) Über die wechselwirkung zwischen wasser und geschiebe in flüssen. Sitzungsberichte der Akademie der Wissenschaften 134(2a):165–203

    Google Scholar 

  • Fredsøe J (1974) On the development of dunes in erodible channels. J Fluid Mech 64:1–16

    Article  Google Scholar 

  • Fredsøe J (1975) The friction factor and height-length relations in flow over a dune-covered bed. Progress report number 37, Institute of Hydrodynamic and Hydraulic Engineering (ISVA), Technical University of Denmark, Kongens Lyngby

    Google Scholar 

  • Fredsøe J, Deigaard R (1992) Mechanics of coastal sediment transport. World Scientific, Singapore

    Google Scholar 

  • Fuchs RA (1951) On the theory of short-crested oscillatory waves. Technical report series HE-116, Volume 326, Institute of Engineering Research, Fluid Mechanics Laboratory, University of California, Berkeley

    Google Scholar 

  • García MH (2008) Sediment transport and morphodynamics. In: García MH (ed) Sedimentation engineering: processes, measurements, modeling, and practice. Manuals and reports on engineering practice number 110, American Society of Civil Engineers, Reston, VA, pp 21–163

    Google Scholar 

  • García MH, Parker G (1993) Experiments on the entrainment of sediment into suspension by a dense bottom current. J Geophys Res 98(C3):4793–4807

    Article  Google Scholar 

  • Gill MA (1971) Height of sand dunes in open channel flows. J Hydraul Div 97(12):2067–2074

    Google Scholar 

  • Guy HP, Simons DB, Richardson EV (1966) Summary of alluvial channel data from flume experiments, 1956–1961. United States geological survey water supply paper number, 462-1, Washington, DC

    Google Scholar 

  • Haaland SE (1983) Simple and explicit formulas for the friction factor in turbulent flow. J Fluids Eng 105(5):89–90

    Article  Google Scholar 

  • Hayashi T (1970) Formation of dunes and antidunes in open channels. J Hydraul Div 96(3):357–366

    Google Scholar 

  • Jaeggi MNR (1984) Formation and effects of alternate bars. J Hydraul Eng 110(2):142–156

    Article  Google Scholar 

  • Julien PY (2010) Erosion and sedimentation, 2nd edn. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Julien PY, Klaassen GJ (1995) Sand-dune geometry of large rivers during floods. J Hydraul Eng 121(9):657–663

    Article  Google Scholar 

  • Julien PY, Raslan Y (1998) Upper-regime plane bed. J Hydraul Eng 124(11):1086–1096

    Article  Google Scholar 

  • Karim F (1995) Bed configuration and hydraulic resistance in alluvial-channel flows. J Hydraul Eng 121(1):15–25

    Article  Google Scholar 

  • Karim F (1999) Bed-form geometry in sand-bed flows. J Hydraul Eng 125(12):1253–1261

    Article  Google Scholar 

  • Karim MF, Kennedy JF (1981) Computer-based predictors for sediment discharge and friction factor of alluvial streams. Report 242, Iowa Institute of Hydraulic Research, University of Iowa, Iowa

    Google Scholar 

  • Keller EA, Melhorn N (1978) Rhythmic spacing and origin of pools and riffles. Geol Soc Am Bull 89(5):723–730

    Article  Google Scholar 

  • Kennedy JF (1961a) Stationary waves and antidunes in alluvial channels. Report number KH-R-2, WM Keck Laboratory of Hydraulics and Water Resources, California Institute of Technology, Pasadena

    Google Scholar 

  • Kennedy JF (1961b) Further laboratory studies of the roughness and suspended load on alluvial streams. Report number KH-R-3, WM Keck Laboratory of Hydraulics and Water Resources, California Institute of Technology, Pasadena

    Google Scholar 

  • Kennedy JF (1963) The mechanics of dunes and antidunes in erodible bed channels. J Fluid Mech 16(4):521–544

    Article  Google Scholar 

  • Knighton DA (1998) Fluvial forms and processes: a new perspective. Arnold, London

    Google Scholar 

  • Lane EW, Kalinske AA (1941) Engineering calculations of suspended sediment. Trans Am Geophys Union 20(3):603–607

    Article  Google Scholar 

  • Laursen EM (1958) The total sediment load of streams. J Hydraul Div 84(1):1–36

    Google Scholar 

  • Liu HK (1957) Mechanics of sediment-ripple formation. J Hydraul Div 83(2):1–23

    Google Scholar 

  • McDonald BC, Banerjee I (1971) Sediments and bed forms on a braided outwash plain. Can J Earth Sci 8(10):1282–1301

    Article  Google Scholar 

  • Meyer-Peter E, Müller R (1948) Formulas for bed-load transport. In: Proceedings of the second meeting of International Association for Hydraulic Research, Stockholm, vol 3, pp 39–64

    Google Scholar 

  • Milne-Thompson LM (1960) Theoretical hydrodynamics. Macmillan, New York

    Google Scholar 

  • Nelson J, Smith CR (1989) Flow in meandering channels with natural topography. In: Ikeda S, Parker G (eds) River meandering. Water resources monograph number 12. American Geophysical Union, Washington, DC, pp 69–102

    Google Scholar 

  • Núñez-González F (2012) Bedload transport of sand-gravel mixtures with antidunes. Flume experiments. PhD thesis, Civil Engineering Faculty, Technical University of Catalonia, Barcelona Tech, Barcelona

    Google Scholar 

  • Núñez-González F, Martín-Vide JP (2011) Analysis of antidune migration direction. J Geophys Res 116(F02004). doi:10.1029/2010JF001761

  • Orgis H (1974) Geschiebebetrieb und bettbildung. Österreichische Ingenieur-Zeitschrift 17(9):285–292

    Google Scholar 

  • Plate EJOF (1957) Laboratory studies on the beginning of sediment ripple formation in an alluvial channel. Master thesis, Colorado State University, Fort Collins, Colorado

    Google Scholar 

  • Ranga Raju KG, Soni JP (1976) Geometry of ripples and dunes in alluvial channels. J Hydraul Res 14(3):241–249

    Article  Google Scholar 

  • Raudkivi AJ (1963) Study of sediment ripple formation. J Hydraul Div 89(6):15–33

    Google Scholar 

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

    Article  Google Scholar 

  • Raudkivi AJ (1990) Loose boundary hydraulics. Pergamon, New York

    Google Scholar 

  • Raudkivi AJ (1997) Ripples on streambed. J Hydraul Eng 123(1):58–64

    Article  Google Scholar 

  • Raupach MR, Antonia RA, Rajagopalan S (1991) Rough-wall turbulent boundary layers. Appl Mech Rev 44(1):1–25

    Article  Google Scholar 

  • Richards KJ (1980) The formation of ripples and dunes on erodible bed. J Fluid Mech 99:597–618

    Article  Google Scholar 

  • Richards KS (1976) The morphology of riffle-pool sequences. Earth Surf Proc Land 1(1):71–88

    Article  Google Scholar 

  • Robert A (1990) Boundary roughness in coarse-grained channels. Prog Phys Geogr 14(1):42–70

    Article  Google Scholar 

  • Simons DB, Richardson EV (1961) Forms of bed roughness in alluvial channels. J Hydraul Div 87(3):87–105

    Google Scholar 

  • Simons DB, Richardson EV (1966) Resistance to flow in alluvial channels. Professional paper 4-J22, United States Geological Survey, Washington, DC

    Google Scholar 

  • Simons DB, Richardson EV, Albertson ML (1961) Flume studies using medium sand (0.45 mm). United States geological survey water supply paper number 1498-A, United States Government Printing Office, Washington, DC

    Google Scholar 

  • Song CCS (1983) Modified kinematic model: application to bed forms. J Hydraul Eng 109(8):1133–1151

    Article  Google Scholar 

  • Southard JB, Boguchwal LA (1990) Bed configurations in steady unidirectional water flows. Part 2. Synthesis of flume data. J Sediment Petrol 60(5):658–679

    Article  Google Scholar 

  • Sukegawa N (1973) Condition for the formation of alternate bars in straight alluvial channels. In: Proceedings of the international symposium of river mechanics, Bangkok, A58:1–11

    Google Scholar 

  • Thackston EL, Krenkel PA (1967) Longitudinal mixing in natural streams. J Sanitary Eng Div 93(5):67–90

    Google Scholar 

  • Tison LH (1949) Origine des ondes de sable et des bancs de sable sous l’action des courants. Transactions of the International Association for Hydraulic Structures Research, Third Meeting, Report II-13, Grenoble

    Google Scholar 

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

  • Tsubaki T, Kawasumi T, Yasutomi T (1953) On the influence of sand ripples upon the sediment transport in open channels. Report, Research Institute for Applied Mechanics, Kyushu University, Japan 2:241–256

    Google Scholar 

  • Valance A (2005) Formation of ripples over a sand bed submitted to a turbulent shear flow. Eur Phys J B 45(3):433–442

    Article  Google Scholar 

  • van den Berg JH, van Gelder A (1993) A new bedform stability diagram, with emphasis on the transition of ripples to plane bed in flows over fine sand and silt. Alluvial Sedimentation, Special publication, International Association of Sedimentologiests 17:11–21

    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

    Google Scholar 

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

    Google Scholar 

  • Watannabe K (1989) A study of bed configurations in alluvial streams. PhD thesis, Kyushu University, Japan

    Google Scholar 

  • Williams PB, Kemp PH (1971) Initiation of ripples on flat sediment beds. J Hydraul Div 97(4):505–522

    Google Scholar 

  • Wright S, Parker G (2004) Flow resistance and suspended load in sand-bed rivers: simplified stratification model. J Hydraul Eng 130(8):796–805

    Article  Google Scholar 

  • Yalin MS (1964) Geometrical properties of sand waves. J Hydraul Div 90(5):105–119

    Google Scholar 

  • Yalin MS (1977) Mechanics of sediment transport. Pergamon, Oxford

    Google Scholar 

  • Yalin MS (1985) On the determination of ripple geometry. J Hydraul Eng 111(8):1148–1155

    Article  Google Scholar 

  • Zhang X-D, Tang L-M, Xu T-Y (2009) Experimental study of flow intensity influence on 2-D sand ripple geometry characteristics. Water Sci Eng 2(4):52–59

    Google Scholar 

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  1. Department of Civil Engineering, Indian Institute of Technology, Kharagpur, India

    Subhasish Dey

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Dey, S. (2014). Bedforms. In: Fluvial Hydrodynamics. GeoPlanet: Earth and Planetary Sciences. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19062-9_8

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