Multiple Time Scales of Fluvial Processes with Bed Load Sediment and Implications for Mathematical Modeling
Publication: Journal of Hydraulic Engineering
Volume 137, Issue 3
Abstract
Fluvial bed load transport is often considered to assume a capacity regime exclusively determined by local flow conditions, but its applicability in naturally occurring unsteady flows remains to be theoretically justified. In addition, mathematical river models are often decoupled, being based on simplified conservation equations and ignoring the feedback impacts of bed deformation to a certain extent. So far whether the decoupling could have considerable impacts on the fluvial processes with bed load transport remains poorly understood. This paper presents a theoretical investigation of both issues. The multiple time scales of fluvial processes with bed load sediment are evaluated to examine the applicability of bed load transport capacity and decoupled models. Numerical case studies involving active bed load transport by highly unsteady flows complement the analysis of the time scales. It is found that bed load transport can sufficiently rapidly adapt to capacity in line with local flow because sediment exchange with the bed overwhelms the advection of bed load sediment by the mean flow. The present work provides theoretical justification of the concept of bed load transport capacity in most circumstances, which is underpinned by existing observations of bed load transport by flash floods. For fluvial processes with bed load transport, the feedback impacts of bed deformation are limited; therefore, decoupled modeling is, in this sense, appropriate.
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Acknowledgments
This work is funded by the Natural Science Foundation of China (Grant Nos. NSFC50739002, NSFC10932012, NSFC10972164), the National Key Basic Research and Development (973) Program of China (Grant No. UNSPECIFIED2007CB714106), and the EU 6th Framework Program under Project HYDRATE (Grant No. UNSPECIFIED037024).
References
Bell, R. G., and Sutherland, A. J. (1983). “Nonequilibrium bedload transport by steady flows.” J. Hydraul. Eng., 109(3), 351–367.
Bhallamudi, S. M., and Chaudhry, M. H. (1991). “Numerical modeling of aggradation and degradation in alluvial channels.” J. Hydraul. Eng., 117(9), 1145–1164.
Cao, Z., Day, R., and Egashira, S. (2002). “Coupled and decoupled numerical modelling of flow and morphological evolution in alluvial rivers.” J. Hydraul. Eng., 128(3), 306–321.
Cao, Z., Li, Y., and Yue, Z. (2007). “Multiple time scales of alluvial rivers carrying suspended sediment and their implications for mathematical modeling.” Adv. Water Resour., 30(4), 715–729.
Cao, Z., Wang, X., Pender, G., and Zhang, S. (2010). “Hydrodynamic modelling in support of flash flood warning.” Proc. ICE Water Manage., 163(7), 327–340.
Capart, H., and Young, D. L. (1998). “Formation of a jump by the dam-break wave over a granular bed.” J. Fluid Mech., 372, 165–187.
Chien, N., and Wan, Z. (1999). Mechanics of sediment transport, ASCE, New York.
Cui, Y., and Parker, G. (2005). “Numerical model of sediment pulses and sediment-supply disturbances in mountain rivers.” J. Hydraul. Eng., 131(8), 646–656.
Cui, Y., Parker, G., and Paola, C. (1996). “Numerical simulation of aggradation and downstream fining.” J. Hydraul. Res., 34(2), 185–204.
de Vries, M. (1965). “Considerations about non-steady bed-load transport in open channels.” Proc., 11th Int. Congress, Int. Association for Hydraulic Research, Delft, The Netherlands, 3.8.1–3.8.11.
de Vries, M. (1973). “River bed variations—Aggradation and degradation.” Proc., Int. Seminars of Hydraulics of Alluvial Streams, Int. Association for Hydraulic Research, Delft, The Netherlands, 1–10.
de Vries, M. (1975). “A morphological time-scale for rivers.” Proc., 16th Int. Congress, Int. Association for Hydraulic Research, Delft, The Netherlands, 2(B3), 17–23.
Duc, B. M., Wenka, T., and Rodi, W. (2004). “Numerical modeling of bed deformation in laboratory channels.” J. Hydraul. Eng., 130(9), 894–904.
Einstein, H. A. (1950). “The bed-load function for sediment transportation in open channel flows.” Technical Bulletin 1026, U.S. Dept. of Agriculture, Washington, DC.
El-Hames, A. S., and Richards, K. S. (1998). “An integrated, physically based model for arid region flash flood prediction capable of simulating dynamic transmission loss.” Hydrol. Processes, 12, 1219–1232.
Gaeuman, D., and Jacobson, R. B. (2007). “Field assessment of alternative bed-load transport estimators.” J. Hydraul. Eng., 133(12), 1319–1328.
Gaweesh, M. T. K., and van Rijn, L. C. (1994). “Bed-load sampling in sand-bed rivers.” J. Hydraul. Eng., 120(12), 1364–1384.
Gomez, B. (1991). “Bedload transport.” Earth-Sci. Rev., 31, 89–132.
Goutiere, L., Soares-Frazao, S., Savary, C., Laraichi, T., and Zech, Y. (2008). “One-dimensional model for transient flows involving bed-load sediment transport and changes in flow regimes.” J. Hydraul. Eng., 134(6), 726–735.
Greimann, B., Lai, Y., and Huang, J. C. (2008). “Two-dimensional total sediment load model equations.” J. Hydraul. Eng., 134(8), 1142–1146.
Holly, F. M., Jr., and Rahuel, J. L. (1990). “New numerical/physical framework for mobile-bed modelling, Part I: Numerical and physical principles.” J. Hydraul. Res., 28(4), 401–416.
Hu, P., and Cao, Z. (2009). “Fully coupled mathematical modelling of turbidity currents over erodible bed.” Adv. Water Resour., 32(1), 1–15.
Jenkins, J., and Hanes, D. (1998). “Collisional sheet flows of sediment driven by a turbulent fluid.” J. Fluid Mech., 370, 29–52.
Kuhnle, R. A. (1992). “Bed load transport during rising and falling stages on two small streams.” Earth Surf. Processes Landforms, 17, 191–197.
Lanzoni, S., Siviglia, A., Frascati, A., and Seminara, G. (2006). “Long waves in erodible channels and morphodynamic influence.” Water Resour. Res., 42, W06D17.
Laronne, J. B., and Reid, I. (1993). “Very high rates of bedload sediment transport by ephemeral desert rivers.” Nature (London), 366(6451), 148–150.
LeVeque, R. (2002). Finite volume methods for hyperbolic problems, Cambridge Univ. Press, Cambridge, UK.
Lyn, D. A. (1987). “Unsteady sediment-transport modeling.” J. Hydraul. Eng., 113(1), 1–15.
Lyn, D. A., and Altinakar, M. (2002). “St. Venant Exner equations for near critical and transcritical flows.” J. Hydraul. Eng., 128(6), 579–587.
Meyer-Peter, E., and Müller, R. (1948). “Formulas for bed-load transport.” Proc., 2nd Congress of Int. Association of Hydraulic Research, Stockholm, Sweden, 39–64.
Mudd, S. M. (2006). “Investigation of the hydrodynamics of flash floods in ephemeral channels: Scaling analysis and simulation using a shock-capturing flow model incorporating the effects of transmission losses.” J. Hydrol. (Amsterdam, Neth.), 324, 65–79.
Phillips, B. C., and Sutherland, A. J. (1989). “Spatial lag effects in bed load sediment transport.” J. Hydraul. Res., 27(1), 115–133.
Phillips, B. C., and Sutherland, A. J. (1990). “Temporal lag effect in bed load sediment transport.” J. Hydraul. Res., 28(1), 5–23.
Rahuel, J. L., Holly, F. M., Jr., Chollet, J. P., Belleudy, P. J., and Yang, G. (1989). “Modeling of riverbed evolution for bedload sediment mixtures.” J. Hydraul. Eng., 115(11), 1521–1542.
Recking, A., Frey, P., Paquier, A., Belleudy, P., and Champagne, J. Y. (2008). “Bed-load transport flume experiments on steep slopes.” J. Hydraul. Eng., 134(9), 1302–1310.
Reid, I., and Laronne, J. B. (1995). “Bed load sediment transport in an ephemeral stream and a comparison with seasonal and perennial counterparts.” Water Resour. Res., 31(3), 773–781.
Reid, I., Laronne, J. B., and Powell, D. M. (1995). “The Nahal Yatir bedload database: Sediment dynamics in a gravel-bed ephemeral stream.” Earth Surf. Processes Landforms, 20, 845–857.
Reid, I., Powell, D. M., and Laronne, J. B. (1996). “Prediction of bed-load transport by desert flash floods.” J. Hydraul. Eng., 122(3), 170–173.
Sieben, J. (1999). “A theoretical analysis of discontinuous flow with mobile bed.” J. Hydraul. Res., 37(2), 199–212.
Song, T., and Graf, W. H. (1997). “Experimental study of bedload transport in unsteady open-channel flow.” Int. J. Sediment Res., 12(3), 63–71.
Sumer, B., Kozakiewicz, A., Fredsoe, J., and Deigaard, R. (1996). “Velocity and concentration profiles in sheet-flow layer of movable bed.” J. Hydraul. Eng., 122(10), 549–558.
Toro, E. F. (2001). Shock-capturing methods for free-surface shallow flows, Wiley, Chichester, England.
van Rijn, L. C. (1993). “Bed material transport, erosion and deposition in non-steady and non-uniform flow.” Chapter 10, Principles of sediment transport in rivers, estuaries and coastal seas, Aqua Publications, Amsterdam.
Wu, W. M. (2007). Computational river dynamics, Taylor & Francis, London.
Wu, W. M., Altinakar, M., and Wang, S. S. Y. (2006). “Depth-average analysis of hysteresis between flow and sediment transport under unsteady conditions.” Int. J. Sediment Res., 21(2), 101–112.
Zhang, R., and Xie, J. (1993). Sedimentation research in China—Systematic selections, China Water and Power, Beijing.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 137 • Issue 3 • March 2011
Pages: 267 - 276
Copyright
© 2011 American Society of Civil Engineers.
History
Received: Oct 29, 2008
Accepted: Jun 23, 2010
Published online: Feb 15, 2011
Published in print: Mar 1, 2011
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