3D Lagrangian modelling of saltating particles diffusion in turbulent water flow

• Autorzy: Bialik R. , Nikora V. , Rowiński P.
• Języki publikacji: EN

Abstrakty

EN

A 3D Lagrangian model of the saltation of solid spherical particles on the bed of an open channel flow, accounting for turbulence-induced mechanisms, is proposed and employed as the key tool of the study. The differences between conventional 2D models and a proposed 3D saltation model are discussed and the advantages of the 3D model are highlighted. Particularly, the 3D model includes a special procedure allowing generation of 3D flow velocity fields. This procedure is based on the assumption that the spectra of streamwise, vertical and transverse velocity components are known at any distance from the bed. The 3D model was used to identify and quantify effects of turbulence on particle entrainment and saltation. The analysis of particle trajectories focused on their diffusive nature, clarifying: (i) the effect of particle mobility parameter; (ii) the effect of bed topography; and (iii) the effect of turbulence. Specifically, the results of numerical simulations describing the abovementioned effects on the change in time of the variance are presented. In addition, the change in time of the skewness and kurtosis, which are likely to reflect the turbulence influence on the spread of particles, are also shown. Two different diffusion regimes (local and intermediate) for each of the investigated flow conditions are confidently identified.

Słowa kluczowe

EN

Lagrangian approach; particle diffusion; particle entrainment; saltating particle trajectories; sediment transport; turbulence-particle interaction

• Wydawca: Instytut Geofizyki PAN ; Springer
• Czasopismo: Acta Geophysica
• Rocznik: 2012
• Tom: Vol. 60, no. 6
• Strony: 1639--1660
• Opis fizyczny: Bibliogr. 41 poz.

Twórcy

autor

Bialik R.

autor

Nikora V.

autor

Rowiński P.

• Institute of Geophysics, Polish Academy of Sciences, Warsaw, Poland,

Bibliografia

• Abbott, J.E., and J.R.D. Francis (1977), Saltation and suspension trajectories of solid grains in a water stream, Phil. Trans. R. Soc. Lond. A 284, 1321, 225-254, DOI: 10.1098/rsta.1977.0009.
• Ancey, C. (2010), Stochastic modeling in sediment dynamics: Exner equation for planar bed incipient bed load transport conditions, J. Geophys. Res. 115, F00A11, DOI: 10.1029/2009JF001260.
• Ancey, C., F. Bigillon, P. Frey, J. Lanier, and R. Ducret (2002), Saltating motion of a bead in a rapid water stream, Phys. Rev. E 66, 036306, DOI: 10.1103/PhysRevE.66.036306.
• Bialik, R.J. (2011a), Particle-particle collision in Lagrangian modelling of saltating grains, J. Hydraul. Res. 49, 1, 23-31, DOI: 10.1080/00221686.2010.543778.
• Bialik, R.J. (2011b), Numerical study of saltation of non-uniform grains, J. Hydraul. Res. 49, 5, 697-701, DOI: 10.1080/00221686.2011.598025.
• Bialik, R.J., V.I. Nikora, P.M. Rowiński, and W. Czernuszenko (2010), A numerical study of turbulence influence on saltating grains. In: A. Dittrich, K. Koll, J. Aberle, and H. Geisenhainer (eds.), Proc. Int. Conf. on River Flow 2010, 08-10.09.2010, Braunschweig, Germany, Bundesanstalt für Wasserbau, Karlsruhe, 105-112.
• Bottacin-Busolin, A., S.J. Tait, A. Marion, A. Chegini, and M. Tregnaghi (2008), Probabilistic description of grain resistance from simultaneous flow field and grain motion measurements, Water Resour. Res. 44, W09419, DOI: 10.1029/2007WR006224.
• Bradley, D.N., G.E. Tucker, and D.A. Benson (2010), Fractional dispersion in a sand bed river, J. Geophys. Res. 115, F00A09, DOI: 10.1029/2009JF001268.
• Crowe, C., M. Sommerfeld, and Y. Tsuji (1998), Multiphase Flows with Droplets and Particles, CRC Press, Boca Raton.
• Drake, T.G., R.L. Shreve, W.E. Dietrich, P.J. Whiting, and L.B. Leopold (1988), Bedload transport of fine gravel observed by motion-picture photography, J. Fluid Mech. 192, 193-217, DOI: 10.1017/S0022112088001831.
• Einstein, H.A. (1937), Der Geschiebebetrieb als Wahrscheinlichkeitsproblem, Verlag Rascher, Zurich.
• Einstein, H.A. (1950), The Bed-Load Function for Sediment Transportation in Open Channel Flows, Tech. Bull. 1026, U.S. Dept. of Agriculture, Washington D.C.
• Ganti, V., M.M. Meerschaert, E. Foufoula-Georgiou, E. Viparelli, and G. Parker (2010), Normal and anomalous diffusion of gravel tracer particles in rivers, J. Geophys. Res. 115, F00A12, DOI: 10.1029/2008JF001222.
• Habersack, H.M. (2001), Radio-tracking gravel particles in a large braided river in New Zealand: a field test of the stochastic theory of bed load transport proposed by Einstein, Hydrol. Process. 15, 3, 377-391, DOI: 10.1002/hyp.147.
• Lee, H.-Y., and I.-S. Hsu (1994), Investigation of saltating particle motion. J. Hydraul. Eng. 120, 7, 831-845, DOI: 10.1061/(ASCE)0733-9429(1994)120:7(831).
• Lee, H.-Y., Y.-H. Chen, J.-Y. You, and Y.-T. Lin (2000), Investigations of continuous bed load saltating process, J. Hydraul. Eng. 126, 9, 691-700, DOI: 10.1061/(ASCE)0733-9429(2000)126:9(691).
• Lee, H.-Y., J.-Y. You, and Y.-T. Lin (2002), Continuous saltating process of multiple sediment particles, J. Hydraul. Eng. 128, 4, 443-450, DOI: 10.1061/(ASCE)0733-9429(2002)128:4(443).
• Lee, H.-Y., Y.-T. Lin, J.-Y. You, and H.-W. Wang (2006), On three-dimensional continuous saltating process of sediment particles near the channel bed, J. Hydraul. Res. 44, 3, 374-389, DOI: 10.1080/00221686.2006.9521689.
• Lukerchenko, N., Z. Chara, and P. Vlasak (2006), 2D numerical model of particlebed collision in fluid-particle flow over bed, J. Hydraul. Res. 44, 1, 70-78, DOI: 10.1080/00221686.2006.9521662.
• Lukerchenko, N., S. Piatsevich, Z. Chara, and P. Vlasak (2009a), 3D numerical model of the spherical particle saltation in a channel with a rough fixed bed, J. Hydrol. Hydromech. 57, 2, 100-112, DOI: 10.2478/v10098-009-0009-x.
• Lukerchenko, N., S. Piatsevich, Z. Chara, and P. Vlasak (2009b), Numerical model of spherical particle saltation in a channel with a transversely tilted rough bed, J. Hydrol. Hydromech. 57, 3, 182-190, DOI: 10.2478/v10098-009-0017-x.
• Marion, A., S.J. Tait, and I. McEwan (2003), Analysis of small-scale gravel bed topography during armoring, Water Resour. Res. 39, 12, 1334, DOI: 10.1029/2003WR002367.
• Murphy, P.J., and H. Hooshiari (1982), Saltation in water dynamics, J. Hydraul. Eng. 108, 11, 1251-1267.
• Nezu, I., and H. Nakagawa (1993), Turbulence in Open-Channel Flows, Balkema, Rotterdam.
• Nikora, V. (1999), Origin of the “–1” spectral law in wall-bounded turbulence, Phys. Rev. Lett. 83, 4, 734-736, DOI: 10.1103/PhysRevLett.83.734.
• Nikora, V. (2005), Flow turbulence over mobile gravel-bed: spectral scaling and coherent structures, Acta Geophys. Pol. 53, 4, 539-552.
• Nikora, V., and D. Goring (2000), Flow turbulence over fixed and weakly mobile gravel beds, J. Hydraul. Eng. 126, 9, 679-690, DOI: 10.1061/(ASCE)0733-9429(2000)126:9(679).
• Nikora, V., J. Heald, D. Goring, and I. McEwan (2001), Diffusion of saltating particles unidirectional water flow over a rough granular bed, J. Phys. A: Math. Gen. 34, L743, DOI: 10.1088/0305-4470/34/50/103.
• Nikora, V., H. Habersack, T. Huber, and I. McEwan (2002), On bed particle diffusion in gravel bed flows under weak bed load transport, Water Resour. Res. 38, 6, DOI: 10.1029/2001WR000513.
• Niño, Y., and M. Garcia (1994), Gravel saltation: 2. Modeling, Water Resour. Res. 30, 6, 1915-1924, DOI: 10.1029/94WR00534.
• Niño, Y., and M. Garcia (1998a), Using Lagrangian particle saltation observations for bedload sediment transport modelling, Hydrol. Process. 12, 8, 1197-1218, DOI: 10.1002/(SICI)1099-1085(19980630)12:8<1197::AIDHYP612>3.0.CO;2-U.
• Niño, Y., and M. Garcia (1998b), Experiments on saltation of sand in water, J. Hydraul. Eng. 124, 10, 1014-1025, DOI: 10.1061/(ASCE)0733-9429(1998)124:10(1014).
• Radice, A., and F. Ballio (2008), Double-average characteristics of sediment motion in one-dimensional bed load, Acta Geophys. 56, 3, 654-668, DOI: 10.2478/s11600-008-0015-0.
• Radice, A., F. Ballio, and V. Nikora (2009), On statistical properties of bed load sediment concentration, Water Resour. Res. 45, W06501, DOI: 10.1029/2008WR007192.
• Radice, A., F. Ballio, and V. Nikora (2010), Statistics and characteristic scales for bed load in a channel flow with sidewall effects, Acta Geophys. 58, 6, 1072-1093, DOI: 10.2478/s11600-010-0020-y.
• Sekine, M., and H. Kikkawa (1992), Mechanics of saltating grains. II, J. Hydraulic Eng. 118, 4, 536-558.
• Tucker, G.E., and D.N. Bradley (2010), Trouble with diffusion: Reassessing hillslope erosion laws with a particle-based model, J. Geophys. Res. 115, F00A10, DOI: 10.1029/2009JF001264.
• Wang, H.W., H.Y. Lee, and P.N. Lee (2009), Three-dimensional saltating process of multiple sediment particles, Int. J. Sediment Res. 24, 1, 16-32, DOI: 10.1016/S1001-6279(09)60013-5.
• Wiberg, P.L., and J.D. Smith (1985), A theoretical model for saltating grains in water, J. Geophys. Res. 90, C4, 7341-7354, DOI: 10.1029/JC090iC04p07341.
• Wong, M., G. Parker, P. DeVries, T.M. Brown, and S.J. Burges (2007), Experiments on dispersion of tracer stones under lower-regime plane-bed equilibrium bed load transport, Water Resour. Res. 43, W03440, DOI: 10.1029/2006WR005172.
• Yen, B.C. (1992), Sediment fall velocity in oscillating flow, Water Resour. Environ. Eng. Res. Rep. 11, Dept. of Civil Eng. University of Virginia.