Mechanics of bed particle saltation in turbulent wall-shear flow. (English) Zbl 1472.86007
Summary: In this paper, we explore the mechanics of bed particle saltation in turbulent wall-shear flow, analysing the forces on a particle to perform saltation. The hydrodynamic drag encompasses the form drag and turbulent drag. The hydrodynamic lift comprises the Saffman lift, Magnus lift and turbulent lift. The subtle role of the Basset force in governing the particle trajectory is accounted for in the analysis. The bedload flux, emanating from the mathematical analysis of bed particle saltation, is determined. The results reveal that for the particle parameter range 20-100, the transport stage function equalling unity corroborates the threshold of bed particle saltation, where the saltation height and length are 1.3 and 9 times the particle size. For a given transport stage function, the relative saltation height and length decrease with an increase in particle parameter. For the particle parameter range 20-100, the relative saltation height and length increase with an increase in transport stage function, reaching their peaks, and then, they decrease. For a given particle parameter, the peak and mean particle densimetric Froude numbers increase as the transport stage function increases. The bedload flux curves for particle parameters 26 and 63 produce the upper and lower bound curves, respectively.
Keywords:
bedload transport; turbulent wall-shear flow; bed particle saltation; geophysics; fluid mechanics; mathematical modellingReferences:
| [1] | Ali SZ, Dey S. 2019 Bed particle saltation in turbulent wall-shear flow: a review. Proc. R. Soc. A 475, 20180824. (10.1098/rspa.2018.0824) · Zbl 1472.86007 |
| [2] | Shao X, Wu T, Yu Z. 2012 Fully resolved numerical simulation of particle-laden turbulent flow in a horizontal channel at a low Reynolds number. J. Fluid Mech. 693, 319-344. (10.1017/jfm.2011.533) · Zbl 1250.76176 |
| [3] | Ji C, Munjiza A, Avital E, Ma J, Williams JJR. 2013 Direct numerical simulation of sediment entrainment in turbulent channel flow. Phys. Fluids 25, 056601. (10.1063/1.4807075) |
| [4] | Kidanemariam AG, Uhlmann M. 2014 Direct numerical simulation of pattern formation in subaqueous sediment. J. Fluid Mech. 750, R2. (10.1017/jfm.2014.284) |
| [5] | Kidanemariam AG, Uhlmann M. 2017 Formation of sediment patterns in channel flow: minimal unstable systems and their temporal evolution. J. Fluid Mech. 818, 716-743. (10.1017/jfm.2017.147) · Zbl 1383.76492 |
| [6] | Chan-Braun C, García-Villalba M, Uhlmann M. 2011 Force and torque acting on particles in a transitionally rough open-channel flow. J. Fluid Mech. 684, 441-474. (10.1017/jfm.2011.311) · Zbl 1241.76393 |
| [7] | Ji C, Munjiza A, Avital E, Xu D, Williams J. 2014 Saltation of particles in turbulent channel flow. Phys. Rev. E 89, 052202. (10.1103/PhysRevE.89.052202) |
| [8] | Elghannay H, Tafti D. 2018 LES-DEM simulations of sediment transport. Int. J. Sedim. Res. 33, 137-148. (10.1016/j.ijsrc.2017.09.006) |
| [9] | Liu D, Liu X, Fu X. In press. LES-DEM simulations of sediment saltation in a rough-wall turbulent boundary layer. J. Hydraul. Res. 57. (10.1080/00221686.2018.1509384) |
| [10] | van Rijn LC. 1984 Sediment transport, part I: bed load transport. J. Hydraul. Eng. 110, 1431-1456. (10.1061/(ASCE)0733-9429(1984)110:10(1431)) |
| [11] | Wiberg PL, Smith JD. 1985 A theoretical model for saltating grains in water. J. Geophys. Res. Oceans 90, 7341-7354. (10.1029/JC090iC04p07341) |
| [12] | Wiberg PL, Smith JD. 1989 Model for calculating bed load transport of sediment. J. Hydraul. Eng. 115, 101-123. (10.1061/(ASCE)0733-9429(1989)115:1(101)) |
| [13] | Niño Y, García M. 1994 Gravel saltation: 2. Modeling. Water Resour. Res. 30, 1915-1924. (10.1029/94WR00534) |
| [14] | Lee H-Y, Hsu I-S. 1994 Investigation of saltating particle motions. J. Hydraul. Eng. 120, 831-845. (10.1061/(ASCE)0733-9429(1994)120:7(831)) |
| [15] | Niño Y, García M. 1998 Using Lagrangian particle saltation observations for bedload sediment transport modelling. Hydrol. Process. 12, 1197-1218. (10.1002/(SICI)1099-1085(19980630)12:8<1197::AID-HYP612>3.0.CO;2-U) |
| [16] | Chen Y, Bai Y, Xu D. 2017 On the mechanisms of the saltating motion of bedload. Int. J. Sedim. Res. 32, 53-59. (10.1016/j.ijsrc.2016.07.001) |
| [17] | Wang H-W, Lee H-Y, Lee P-N. 2009 Three-dimensional saltating processes of multiple sediment particles. Int. J. Sedim. Res. 24, 16-32. (10.1016/S1001-6279(09)60013-5) |
| [18] | Dey S. 2014 Fluvial hydrodynamics: hydrodynamic and sediment transport phenomena. Berlin, Germany: Springer. |
| [19] | Brush LM, Ho H-W, Yen B-C. 1964 Accelerated motion of a sphere in a viscous fluid. J. Hydraul. Div. 90, 149-160. |
| [20] | Owen PR. 1964 Saltation of uniform grains in air. J. Fluid Mech. 20, 225-242. (10.1017/S0022112064001173) · Zbl 0151.42703 |
| [21] | White BR, Schultz JC. 1977 Magnus effect in saltation. J. Fluid Mech. 81, 497-512. (10.1017/S0022112077002183) |
| [22] | Bialik RJ. 2015 Lagrangian modelling of saltating sediment transport: a review. In Rivers—physical, fluvial and environmental processes (eds P Rowiński, A Radecki-Pawlik), pp. 427-441. Berlin, Germany: Springer. (10.1007/978-3-319-17719-9_16) |
| [23] | Bagnold RA. 1937 The transport of sand by wind. Geogr. J. 89, 409-438. (10.2307/1786411) |
| [24] | Anderson RS, Haff PK. 1988 Simulation of eolian saltation. Science 241, 820-823. (10.1126/science.241.4867.820) |
| [25] | Bagnold RA. 1973 The nature of saltation and of ‘bedload’ transport in water. Proc. R. Soc. Lond. A 332, 473-504. (10.1098/rspa.1973.0038) |
| [26] | Francis JRD. 1973 Experiments on the motion of solitary grains along the bed of a water-stream. Proc. R. Soc. Lond. A 332, 443-471. (10.1098/rspa.1973.0037) |
| [27] | Dey S, Ali SZ. 2019 Bed sediment entrainment by streamflow: state of the science. Sedimentology 66, 1449-1485. (10.1111/sed.12566) |
| [28] | Dey S, Ali SZ. 2018 Review article: advances in modeling of bed particle entrainment sheared by turbulent flow. Phys. Fluids 30, 061301. (10.1063/1.5030458) |
| [29] | Cao Z, Pender G, Meng J. 2006 Explicit formulation of the Shields diagram for incipient motion of sediment. J. Hydraul. Eng. 132, 1097-1099. (10.1061/(ASCE)0733-9429(2006)132:10(1097)) |
| [30] | Ali SZ, Dey S. 2016 Hydrodynamics of sediment threshold. Phys. Fluids 28, 075103. (10.1063/1.4955103) |
| [31] | Yen BC. 1992 Sediment fall velocity in oscillating flow. Water Resources and Environmental Engineering Research Report, issue 11. Department of Civil Engineering, University of Virginia, Charlottesville, VA, USA. |
| [32] | Taylor GI. 1935 Statistical theory of turbulence. Proc. R. Soc. Lond. A 151, 421-444. (10.1098/rspa.1935.0158) · JFM 61.0926.02 |
| [33] | Nezu I, Nakagawa H. 1993 Turbulence in open-channel flows. Rotterdam, The Netherlands: Balkema. · Zbl 0358.76042 |
| [34] | Saffman PG. 1965 The lift on a small sphere in a slow shear flow. J. Fluid Mech. 22, 385-400. (10.1017/S0022112065000824) · Zbl 0218.76043 |
| [35] | Saffman PG. 1968 Corrigendum, the lift on a small sphere in a slow shear flow. J. Fluid Mech. 31, 624. (10.1017/S0022112068999990) |
| [36] | Rubinow SI, Keller JB. 1961 The transverse force on a spinning sphere moving in a viscous fluid. J. Fluid Mech. 11, 447-459. (10.1017/S0022112061000640) · Zbl 0103.19503 |
| [37] | Nezu I. 1977 Turbulent structure in open channel flow. PhD thesis, Kyoto University, Kyoto, Japan. · Zbl 0358.76042 |
| [38] | Grass AJ. 1971 Structural features of turbulent flow over smooth and rough boundaries. J. Fluid Mech. 50, 233-255. (10.1017/S0022112071002556) |
| [39] | Abbott JE, Francis JRD. 1977 Saltation and suspension trajectories of solid grains in a water stream. Phil. Trans. R. Soc. Lond. A 284, 225-254. (10.1098/rsta.1977.0009) |
| [40] | Niño Y, García M. 1998 Experiments on saltation of sand in water. J. Hydraul. Eng. 124, 1014-1025. (10.1061/(ASCE)0733-9429(1998)124:10(1014)) |
| [41] | Auel C, Albayrak I, Sumi T, Boes RM. 2017 Sediment transport in high-speed flows over a fixed bed: 1. Particle dynamics. Earth Surf. Proc. Landf. 42, 1365-1383. (10.1002/esp.4128) |
| [42] | Auel C, Albayrak I, Sumi T, Boes RM. 2017 Sediment transport in high-speed flows over a fixed bed: 2. Particle impacts and abrasion prediction. Earth Surf. Proc. Landf. 42, 1384-1396. (10.1002/esp.4132) |
| [43] | Hu C, Hui Y. 1996 Bed-load transport. I: mechanical characteristics. J. Hydraul. Eng. 122, 245-254. (10.1061/(ASCE)0733-9429(1996)122:5(245)) |
| [44] | Ancey C, Bigillon F, Frey P, Lanier J, Ducret R. 2002 Saltating motion of a bead in a rapid water stream. Phys. Rev. E 66, 036306. (10.1103/PhysRevE.66.036306) |
| [45] | Ramesh B, Kothyari UC, Murugesan K. 2011 Near-bed particle motion over transitionally-rough bed. J. Hydraul. Res. 49, 757-765. (10.1080/00221686.2011.620369) |
| [46] | Niño Y, García M, Ayala L. 1994 Gravel saltation: 1. Experiments. Water Resour. Res. 30, 1907-1914. (10.1029/94WR00533) |
| [47] | Lee H-Y, Chen Y-H, You J-Y, Lin Y-T. 2000 Investigations of continuous bed load saltating process. J. Hydraul. Eng. 126, 691-700. (10.1061/(ASCE)0733-9429(2000)126:9(691)) |
| [48] | Chatanantavet P, Whipple KX, Adams MA, Lamb MP. 2013 Experimental study on coarse grain saltation dynamics in bedrock channels. J. Geophys. Res. Earth Surf. 118, 1161-1176. (10.1002/jgrf.20053) |
| [49] | Bhattacharyya A, Ojha SP, Mazumder BS. 2013 Evaluation of the saltation process of bed materials by video imaging under altered bed roughness. Earth Surf. Proc. Landf. 38, 1339-1353. (10.1002/esp.3370) |
| [50] | Fernandez Luque R, van Beek R. 1976 Erosion and transport of bed-load sediment. J. Hydraul. Res. 14, 127-144. (10.1080/00221687609499677) |
| [51] | Meyer-Peter E, Favre H, Einstein HA. 1934 Neuere versuchsresultate über den geschiebetrieb. Schweiz. Bauztg. 103, 147-150. |
| [52] | Casey HJ. 1935 Über geschiebebewegung. In Mitteilungen der Preussischen Versuchsanstalt für Wasserbau und Schiffbau, Berlin, Germany. |
| [53] | Mavis FT, Liu T, Soucek E. 1937 The transportation of detritus by flowing water-II. University of Iowa: Iowa, USA. |
| [54] | Yung HP. 1939 Abhangigkeit der geschiebebewegung von der kornform und der temperature. In Mitteilungen der Preussischen Versuchsanstaltt für Wasserbau und Schiffbau, Berlin, Germany. |
| [55] | Einstein HA. 1942 Formulas for the transportation of bed load. Trans. Am. Soc. Civ. Eng. 107, 561-577. |
| [56] | Meyer-Peter E, Müller R. 1948 Formulas for bed-load transport. In Proc. of the 2nd Meeting of Int. Association for Hydraulic Research, Stockholm, Sweden, 7-9 June, vol. 3, pp. 39-64. Madrid, Spain: IAHR. |
| [57] | Smart GM. 1984 Sediment transport formula for steep channels. J. Hydraul. Eng. 110, 267-276. (10.1061/(ASCE)0733-9429(1984)110:3(267)) |
| [58] | Recking A. 2006 An experimental study of grain sorting effects on bedload. PhD thesis, University of Lyon, Lyon, France. |
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