Flow Resistance for a Varying Density of Obstacles on Smooth and Rough Beds
Publication: Journal of Hydraulic Engineering
Volume 146, Issue 2
Abstract
High-return-period floods involve complex flows over large floodplains covered with different types of resistive elements, from bed roughness to large emerging obstacles. In order to characterize the flow resistance in such configurations, experiments are conducted in a flume with emergent aligned obstacles on smooth and rough beds. Under uniform flow conditions, the drag force is measured by a hydrodynamic force measurement device, thereby obtaining the relative contribution of the drag and bed friction forces to the total flow resistance. The results show a strong correlation between the reference surface ratio (), i.e., the obstacle frontal area divided by the cell bed surface, and the relative contribution of the drag to the flow resistance, with negligible influence of bed roughness and shallowness. Equal contributions of bed roughness and form drag to flow resistance occur for . After showing that the drag coefficient is roughly constant and the bed friction is consistent with Darcy-Weisbach’s head-loss coefficient, a Chezy-type equation is proposed to predict the mean uniform velocity as a function of the flow and land occupation parameters.
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Data Availability Statement
All data shown in this article are available from the corresponding author by request. The database consists of: (1) normal depth and discharge for all experiments, (2) drag force measurements, (3) water surface oscillations to characterize seiches, and (4) time-average velocity measurements.
Acknowledgments
This project was founded by the French National Research Agency project FLOWRES (ANR-14-CE03-0010). The authors also want to acknowledge the participation Cedric Marmounier in the design and construction of the hydrodynamic force measurement device and Zineb Mrabet-Kandri for her contribution on the smooth bed experiments.
References
Abrahams, A. D., and A. J. Parsons. 1994. “Hydraulics of interrill overland flow on stone-covered desert surfaces.” Catena 23 (1–2): 111–140. https://doi.org/10.1016/0341-8162(94)90057-4.
Baptist, M. J., V. Babovic, J. Rodríguez Uthurburu, M. Keijzer, R. E. Uittenbogaard, A. Mynett, and A. Verwey. 2007. “On inducing equations for vegetation resistance.” J. Hydraul. Res. 45 (4): 435–450. https://doi.org/10.1080/00221686.2007.9521778.
Blevins, R. D. 1984. Applied Fluid Dynamics Handbook. New York: Van Nostrand Reinhold Co.
Cassan, L., T. D. Tien, D. Courret, P. Laurens, and D. Dartus. 2014. “Hydraulic resistance of emergent macroroughness at large Froude numbers: Design of nature-like fishpasses.” J. Hydraul. Eng. 140 (9): 04014043. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000910.
Cheng, N.-S., and H. T. Nguyen. 2011. “Hydraulic radius for evaluating resistance induced by simulated emergent vegetation in open-channel flows.” J. Hydraul. Eng. 137 (9): 995–1004. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000377.
Colebrook, C. F., and C. M. White. 1937. “Experiments with fluid friction in roughened pipes.” Proc. R. Soc. A: Math. Phys. Eng. Sci. 161 (906): 367–381. https://doi.org/10.1098/rspa.1937.0150.
Dupuis, V., S. Proust, C. Berni, and A. Paquier. 2016. “Combined effects of bed friction and emergent cylinder drag in open channel flow.” Environ. Fluid Mech. 16 (6): 1173–1193. https://doi.org/10.1007/s10652-016-9471-2.
Herbich, J. B., and S. Shulits. 1964. “Large scale roughness in open-channel flow.” J. Hydraul. Div. 90 (6): 203–230.
Hirabayashi, Y., R. Mahendran, S. Koirala, L. Konoshima, D. Yamazaki, S. Watanabe, H. Kim, and S. Kanae. 2013. “Global flood risk under climate change.” Nat. Clim. Change 3 (Jun): 816–821. https://doi.org/10.1038/nclimate1911.
Huthoff, F., D. C. M. Augustijn, and S. J. M. H. Hulscher. 2007. “Analytical solution of the depth-averaged flow velocity in case of submerged rigid cylindrical vegetation.” Water Resour. Res. 43 (6): 1–10. https://doi.org/10.1029/2006WR005625.
Ishikawa, Y., K. Mizuhara, and S. Ashida. 2000. “Effect of density of trees on drag exerted on trees in river channels.” J. For. Res. 5 (4): 271–279. https://doi.org/10.1007/BF02767121.
James, C. S., A. L. Birkhead, A. A. Jordanova, and J. J. O’Sullivan. 2004. “Flow resistance of emergent vegetation.” J. Hydraul. Res. 42 (4): 390–398. https://doi.org/10.1080/00221686.2004.9728404.
Lang, M., K. Pobanz, B. Renard, E. Renouf, and E. Sauquet. 2010. “Extrapolation of rating curves by hydraulic modelling, with application to flood frequency analysis.” Hydrol. Sci. J. 55 (Aug): 883–898. https://doi.org/10.1080/02626667.2010.504186.
Lawrence, D. S. L. 1997. “Macroscale surface roughness and frictional resistance in overland flow.” Earth Surf. Processes Landforms 22 (4): 365–382. https://doi.org/10.1002/(SICI)1096-9837(199704)22:4%3C365::AID-ESP693%3E3.0.CO;2-6.
Lawrence, D. S. L. 2000. “Hydraulic resistance in overland flow during partial and marginal surface inundation: Experimental observations and modeling.” Water Resour. Res. 36 (8): 2381–2393. https://doi.org/10.1029/2000WR900095.
Marshall, J. 1971. “Drag measurements in roughness arrays of varying density and distribution.” Agric. Meteorol. 8: 269–292. https://doi.org/10.1016/0002-1571(71)90116-6.
Moody, L. F. 1944. “Friction factors for pipe flow.” Trans. ASME 66 (8): 671–684.
Mustafa, A., M. Bruwier, J. Teller, P. Archambeau, S. Erpicum, M. Pirotton, and B. Dewals. 2016. “Impacts of urban expansion on future flood damage: A case study in the River Meuse basin, Belgium.” In Sustainable Hydraulics in the Era of Global Change, 856–862. Liege, Belgium: CRC Press.
Nepf, H. M. 1999. “Drag, turbulence, and diffusion in flow through emergent vegetation.” Water Resour. Res. 35 (2): 479–489. https://doi.org/10.1029/1998WR900069.
Papanicolaou, A. N., D. C. Dermisis, and M. Elhakeem. 2011. “Investigating the role of clasts on the movement of sand in gravel bed rivers.” J. Hydraul. Eng. 137 (9): 871–883. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000381.
Papanicolaou, A. N., C. M. Kramer, A. G. Tsakiris, T. Stoesser, S. Bomminayuni, and Z. Chen. 2012. “Effects of a fully submerged boulder within a boulder array on the mean and turbulent flow fields: Implications to bedload transport.” Acta Geophys. 60 (6): 1502–1546. https://doi.org/10.2478/s11600-012-0044-6.
Raupach, M. R. 1992. “Drag and drag partition on rough surfaces.” Boundary Layer Meteorol. 60 (4): 375–395. https://doi.org/10.1007/BF00155203.
Raupach, M. R., D. A. Gillette, and J. F. Leys. 1993. “The effect of roughness elements on wind erosion threshold.” J. Geophys. Res.: Atmos. 98 (D2): 3023–3029. https://doi.org/10.1029/92JD01922.
Ricardo, A. M., M. J. Franca, and R. M. L. Ferreira. 2016. “Turbulent flows within random arrays of rigid and emergent cylinders with varying distribution.” J. Hydraul. Eng. 142 (9): 04016022. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001151.
Schlichting, H. 1936. “Experimentelle Untersuchungen zum Rauhigkeitsproblem (Experimental investigation of the problem of surface roughness)” Ing. Arch. 7 (1): 1–34. https://doi.org/10.1007/BF02084166.
Shields, F. D., K. G. Coulton, and H. Nepf. 2017. “Representation of vegetation in two-dimensional hydrodynamic models.” J. Hydraul. Eng. 143 (8): 02517002. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001320.
Tanino, Y. 2008. “Flow and solute transport in random cylinder arrays: A model for emergent aquatic plant canopies.” Ph.D. dissertation, Dept. of Civil and Environmental Engineering, Massachusetts Institute of Technology.
Tanino, Y., and H. M. Nepf. 2008. “Laboratory investigation of mean drag in a random array of rigid, emergent cylinders.” J. Hydraul. Eng. 134 (Jan): 34–41. https://doi.org/10.1061/(ASCE)0733-9429(2008)134:1(34).
Tsakiris, A. G., A. N. T. Papanicolaou, S. M. Hajimirzaie, and J. H. J. Buchholz. 2014. “Influence of collective boulder array on the surrounding time-averaged and turbulent flow fields.” J. Mt. Sci. 11 (6): 1420–1428. https://doi.org/10.1007/s11629-014-3055-8.
Wooding, R. A., E. F. Bradley, and J. K. Marshall. 1973. “Drag due to regular arrays of roughness elements of varying geometry.” Boundary Layer Meteorol. 5 (3): 285–308. https://doi.org/10.1007/BF00155238.
Wyatt, V. E., and W. G. Nickiing. 1997. “Drag and shear stress partitioning in sparse desert creosote communities.” Can. J. Earth Sci. 34 (11): 1486–1498. https://doi.org/10.1139/e17-121.
Yager, E. M., J. W. Kirchner, and W. E. Dietrich. 2007. “Calculating bed load transport in steep boulder bed channels.” Water Resour. Res. 43 (7): 1–24. https://doi.org/10.1029/2006WR005432.
Zhao, K., N.-S. Cheng, and Z. Huang. 2014. “Experimental study of free-surface fluctuations in open-channel flow in the presence of periodic cylinder arrays.” J. Hydraul. Res. 52 (4): 465–475. https://doi.org/10.1080/00221686.2014.880858.
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Information
Published In
Journal of Hydraulic Engineering
Volume 146 • Issue 2 • February 2020
Copyright
©2019 American Society of Civil Engineers.
History
Received: Oct 12, 2018
Accepted: Jun 17, 2019
Published online: Dec 6, 2019
Published in print: Feb 1, 2020
Discussion open until: May 6, 2020
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