Spatial Variability in the Motion of a Rolling Bead due to a Step in Bed Roughness
Publication: Journal of Engineering Mechanics
Volume 149, Issue 1
Abstract
The impact of the sudden change in bed roughness due to a cluster of motionless, submerged bed-mounted posts on the dynamics of a coarse sphere transported by the turbulent flow as bed load was experimentally and analytically studied. The rolling motion of the bead upstream of the cluster, in almost straight paths at a virtually constant velocity, switched abruptly to a spatially varied, highly perturbed motion as soon as the particle moved through the cluster interstices, following tortuous path and performing cycles of strong decelerations (due to collisions) and accelerations (due to the drag force). Analysis of measurements in terms of a simplified initial value problem showed that the slowdown of the mean velocity of the sphere depends on the mean flow velocity in the rough layer, the geometrical constraint imposed by the mean interstitial length, the features of the collisional interaction, and the bead diameter and density.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All data and the model generated and used during the study appear in the published article and are available.
Acknowledgments
Román Martino gratefully acknowledges support from BID PICT 2019-02423 grant.
References
Ancey, C. 2020a. “Bedload transport: A walk between randomness and determinism. Part 1. The state of the art.” J. Hydraul. Res. 58 (1): 1–17. https://doi.org/10.1080/00221686.2019.1702594.
Ancey, C. 2020b. “Bedload transport: A walk between randomness and determinism. Part 2. Challenges and prospects.” J. Hydraul. Res. 58 (1): 18–33. https://doi.org/10.1080/00221686.2019.1702595.
Ancey, C., F. Bigillon, P. Frey, and R. Ducret. 2003. “Rolling motion of a bead in a rapid water stream.” Phys. Rev. E 67 (1): 011303. https://doi.org/10.1103/PhysRevE.67.011303.
Bounvilay, B., and P. Julien. 2013. “Velocity of rolling bed load particles.” J. Hydraul. Eng. 139 (2): 177–186. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000657.
Chen, Z., C. Jiang, and H. Nepf. 2013. “Flow adjustment at the leading edge of a submerged aquatic canopy.” Water Resour. Res. 49 (9): 5537–5551. https://doi.org/10.1002/wrcr.20403.
Cheng, N., and A. Emadzadeh. 2014. “Average velocity of solitary coarse grain in flows over smooth and rough beds.” J. Hydraul. Eng. 140 (6): 04014015. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000875.
Chhabra, R. P., and J. M. Ferreira. 1999. “An analytical study of the motion of a sphere rolling down a smooth inclined plane in an incompressible Newtonian fluid.” Powder Technol. 104 (2): 130–138. https://doi.org/10.1016/S0032-5910(99)00032-7.
Curran, J. C., and L. Tan. 2014. “The effect of cluster morphology on the turbulent flows over an armored gravel bed surface.” J. Hydro-environ. Res. 8 (2): 129–142. https://doi.org/10.1016/j.jher.2013.11.002.
Etminan, V., R. Lowe, and M. Ghisalberti. 2017. “A new model for predicting the drag exerted by vegetation canopies.” Water Resour. Res. 53 (4): 3179–3196. https://doi.org/10.1002/2016WR020090.
Ghilardi, T., M. J. Franca, and A. J. Schleiss. 2014. “Sediment transport in steep channels with large roughness elements.” In River flow 2014, edited by A. J. Schleiss. London: Taylor and Francis Group.
Ghisalberti, M., and H. Nepf. 2009. “Shallow flows over a permeable medium: The hydrodynamics of submerged aquatic canopies.” Transp. Porous Media 78 (2): 309–326. https://doi.org/10.1007/s11242-008-9305-x.
Gondret, P., M. Lance, and L. Petit. 2002. “Bouncing motion of spherical particles in fluids.” Phys Fluids 14 (2): 643. https://doi.org/10.1063/1.1427920.
Grams, P. E., and P. R. Wilcock. 2015. “Transport of fine sediment over a coarse, immobile riverbed.” J. Geophys. Res. Earth Surf. 119 (2): 188–211. https://doi.org/10.1002/2013JF002925.
Heyman, J., P. Bohorquez, and C. Ancey. 2016. “Entrainment, motion, and deposition of coarse particles transported by water over a sloping mobile bed.” J. Geophys. Res. Earth Surf. 121 (10): 1931–1952. https://doi.org/10.1002/2015JF003672.
Kuhnle, R. A., D. G. Wren, E. J. Langendoen, and J. R. Rigby. 2013. “Sand transport over an immobile gravel substrate.” J. Hydraul. Eng. 139 (2): 167–176. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000615.
Lajeunesse, E., O. Devauchelle, and F. James. 2018. “Advection and dispersion of bed load tracers.” Earth Surf. Dyn. 6 (2): 389–399. https://doi.org/10.5194/esurf-6-389-2018.
Lajeunesse, E., L. Malverti, and F. Charru. 2010. “Bed load transport in turbulent flow at the grain scale: Experiments and modeling.” J. Geophys. Res. Earth Surf. 115 (4): 1–16. https://doi.org/10.1029/2009JF001628.
Li, Z., D. Chen, H. Sun, Z. Meng, Y. Zhang, and R. T. Sibatov. 2021. “Analyzing and modeling sub-diffusive transport of bedload along a heterogeneous gravel bed using stochastic and statistical methods.” J. Hydrol. 596 (May): 125697. https://doi.org/10.1016/j.jhydrol.2020.125697.
Liu, L., Z. Hu, J. Lei, and H. Nepf. 2018. “Vortex structure and sediment deposition in the wake behind a finite patch of model submerged vegetation.” J. Hydraul. Eng. 144 (2): 04017065. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001408.
Martino, R., J. Estergaard Jacobsen, A. Paterson, and M. Piva. 2020. “Decrease of streamwise mean velocity of single spheres due to presence of a sparse network of immobile bed-mounted particles.” J. Eng. Mech. 146 (11): 04020130. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001863.
Martino, R., A. Paterson, and M. Piva. 2013. “Water level rise upstream a permeable barrier in subcritical flow: Experiment and modeling.” J. Fluids Eng. 136 (4): 041103. https://doi.org/10.1115/1.4026356.
Nepf, H., and M. Ghisalberti. 2008. “Flow and transport in channels with submerged vegetation.” Acta Geophys. 56 (3): 753–777. https://doi.org/10.2478/s11600-008-0017-y.
Okamoto, T., and I. Nezu. 2013. “Spatial evolution of coherent motions in finite-length vegetation patch flow.” Environ. Fluid Mech. 13 (5): 417–434. https://doi.org/10.1007/s10652-013-9275-6.
Papanicolaou, A. N., P. Diplas, C. L. Dancey, and M. Balakrishnan. 2001. “Surface roughness effects in near-bed turbulence: Implications to sediment entrainment.” J. Eng. Mech. 127 (3): 211–218. https://doi.org/10.1061/(ASCE)0733-9399(2001)127:3(211).
Papanicolaou, A. N., A. Tsakiris, M. Wyssmann, and C. Kramer. 2018. “Boulder array effects on bedload pulses and depositional patches.” J. Geophys. Res. Earth Surf. 123 (11): 2925–2953. https://doi.org/10.1029/2018JF004753.
Radice, A., and J. Campagnol. 2015. “How do macro-roughness elements affect bed-load sediment motion?” In Vol. 17 of EGU general assembly, EGU2015. Vienna, Austria: European Geosciences Union.
Rulot, F., B. J. Dewals, S. Erpicum, P. Archambeau, and M. Pirotton. 2011. “Modelling sediment transport over partially non-erodible bottoms.” Int. J. Numer. Methods Fluids 70 (2): 186–199. https://doi.org/10.1002/fld.2684.
Sonnenwald, F., V. Stovin, and I. Guymer. 2019. “Estimating drag coefficient for arrays of rigid cylinders representing emergent vegetation.” J. Hydraul. Res. 57 (4): 591–597. https://doi.org/10.1080/00221686.2018.1494050.
Steidtmann, J. 1982. “Size-density sorting of sand-size spheres during deposition from bedload transport and implications concerning hydraulic equivalence.” Sedimentology 29 (6): 877–883. https://doi.org/10.1111/j.1365-3091.1982.tb00090.x.
Tan, L., and J. Curran. 2012. “Comparison of turbulent flows over clusters of varying density.” J. Hydraul. Eng. 38 (12): 1031–1044. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000635.
Wang, W.-J., W.-X. Huai, S. Thompson, and G. G. Katul. 2015. “Steady nonuniform shallow flow within emergent vegetation.” Water Resour. Res. 51 (12): 10047–10064. https://doi.org/10.1002/2015WR017658.
Wilcock, P. R., and B. W. McArdell. 1997. “Partial transport of a sand-gravel sediment.” Water Resour. Res. 33 (1): 233–245. https://doi.org/10.1029/96WR02672.
Yu, Z., D. Wang, and X. Liu. 2019. “Impact of vegetation density on the wake structure.” Water 11 (6): 1266. https://doi.org/10.3390/w11061266.
Zdravkovich, M. M. 2003. Flow around circular cylinders: Volume 2: Applications. Oxford, UK: Oxford Science Publications.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 149 • Issue 1 • January 2023
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Feb 24, 2022
Accepted: Jul 20, 2022
Published online: Oct 18, 2022
Published in print: Jan 1, 2023
Discussion open until: Mar 18, 2023
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.