Modeling of Spatial Lag in Bed-Load Transport Processes and Its Effect on Dune Morphology
Publication: Journal of Hydraulic Engineering
Volume 143, Issue 2
Abstract
In the present study, two bed-load transport models are introduced in an existing idealized dune model. These allow for the modeling of the spatial lag between the sediment transport rate and bed shear stress along dune surfaces. This lag is an important factor in determining transitions between bedform regimes. Results of the original dune model (using an equilibrium transport formula) are compared with (1) a new model version that directly models spatial lag with a relaxation equation and (2) a new model version including pick-up and deposition processes. Both bed-load models use mean particle step length as an important parameter, which is varied to assess which value is appropriate for the dune regime. Laboratory experiments are simulated with the model. This shows that the results are best with the pick-up and deposition model version, combined with a step length of 25 times the particle diameter. It is furthermore shown that in principle the model is also able to wash out fully grown dunes, by increasing the step length parameter.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This study was carried out as part of the project BedFormFlood, supported by the Technology Foundation STW, the applied science division of now, and the technology program of the Ministry of Economic Affairs.
References
Allen, J. R. L. (1974). “Reaction, relaxation and lag in natural sedimentary system: General principles, examples and lessons.” Earth Sci. Rev., 10(4), 263–342.
Allen, J. R. L. (1978). “Computational methods for dune time-lag: Calculations using Stein’s rule for dune height.” Sediment. Geol., 20(3), 165–216.
Best, J. (2005). “The fluid dynamics of river dunes: A review and some future research directions.” J. Geophys. Res., 110(F4), F04S02.
Casas, A., Benito, G., Thorndycraft, V. R., and Rico, M. (2006). “The topographic data source of digital terrain models as a key element in the accuracy of hydraulic flood modelling.” Earth Surf. Processes Land Forms, 31(4), 444–456.
Colombini, M., and Stocchino, A. (2012). “Three-dimensional river bedforms.” J. Fluid Mech., 695, 63–80.
Einstein H. A. (1950). “The bed load function for sediment transportation in open channel flows.”, U.S. Dept. of Agriculture, Soil Conservation Service, Washington, DC.
Engelund, F. (1966). “Hydraulic resistance of alluvial streams.” J. Hydraul. Div., 92(2), 315–326.
Engelund, F. (1970). “Instability of erodible beds.” J. Fluid Mech., 42(02), 225–244.
Engelund, F., and Fredsøe, J. (1974). “Transition from dunes to plane bed in alluvial channels.” Institute of Hydrodynamics and Hydraulic Engineering, Technical Univ. of Denmark, Lyngby, Denmark.
Fernandez Luque, R., and Van Beek, R. (1976). “Erosion and transport of bed sediment.” J. Hydraul. Res., 14(2), 127–144.
Francis, J. R. D. (1973). “Experiment on the motion of solitary grains along the bed of a water stream.” Proc., Royal Society of London A, Vol. 332, Royal Society, London, 443–471.
Fredsøe, J. (1974). “On the development of dunes in erodible channels.” J. Fluid Mech., 64(01), 1–16.
Fredsøe, J., and Deigaard, R. (1992). “Mechanics of coastal sediment transport.” Advanced series on ocean engineering, Vol. 3, World Scientific, Singapore.
Hulscher, S. J. M. H. (1996). “Tidal-induced large-scale regular bedform patterns in a three-dimensional shallow water model.” J. Geophys. Res., 101(C9), 20727–20744.
Jerolmack, D. J., and Mohrig, D. (2005). “A unified model for subaqueous bedform dynamics.” Water Resour. Res., 41(12), W12421.
Julien, P. Y., and Klaassen, G. J. (1995). “Sand-dune geometry of large rivers during floods.” J. Hydraul. Eng., 657–663.
Kennedy, J. F. (1963). “The mechanics of dunes and antidunes in erodible-bed channels.” J. Fluid Mech., 16(04), 521–544.
Kleinhans, M. G., Wilbers, A. W. E., and Ten Brinke, W. B. M. (2007). “Opposite hysteresis of sand and gravel transport upstream and downstream of a bifurcation during a flood in the River Rhine, the Netherlands.” Neth. J. Geosci., 86(3), 273–285.
Kostaschuk, R. (2000). “A field study of turbulence and sediment dynamics over subaqueous dunes with flow separation.” Sedimentology, 47(3), 519–531.
Kroy, K., Sauermann, G., and Herrmann, H. J. (2002). “Minimal model for aeolian sand dunes.” Phys. Rev. E, 66(3), 031302.
Meyer-Peter, E., and Müller, R. (1948). “Formulas for bed-load transport.” Proc., 2nd IAHR Congress, Vol. 2, IAHR, Madrid, Spain, 39–64.
Morvan, H., Knight, D., Wright, N., Tang, X., and Crossley, A. (2008). “The concept of roughness in fluvial hydraulics and its formulation in 1D, 2D and 3D numerical simulation models.” J. Hydraul. Res., 46(2), 191–208.
Nabi, M., de Vriend, H. J., Mosselman, E., Sloff, C. J., and Shimizu, Y. (2012). “Detailed simulation of morphodynamics. 1: Hydrodynamics model.” Water Resour. Res., 48(12), W12523.
Nabi, M., de Vriend, H. J., Mosselman, E., Sloff, C. J., and Shimizu, Y. (2013a). “Detailed simulation of morphodynamics. 2: Sediment pickup, transport, and deposition.” Water Resour. Res., 49(8), 4775–4791.
Nabi, M., de Vriend, H. J., Mosselman, E., Sloff, C. J., and Shimizu, Y. (2013b). “Detailed simulation of morphodynamics. 3: Ripples and dunes.” Water Resour. Res., 49(9), 5930–5943.
Nakagawa, H., and Tsujimoto, T. (1980). “Sand bed instability due to bed load motion.” J. Hydraul. Div., 106(12), 2029–2051.
Nelson, J. M., Burman, A. R., Shimizu, Y., McLean, S. R., Shreve, R. L., and Schmeeckle, M. (2005). “Computing flow and sediment transport over bedforms.” River, Coastal and Estuarine Morphodynamics: RCEM 2005, Taylor & Francis Group, London, 861–872.
Németh, A. A., Hulscher, S. J. M. H., and Van Damme, R. M. J. (2006). “Simulating offshore sand waves.” Coastal Eng., 53(2–3), 265–275.
Paarlberg, A. J., Dohmen-Janssen, C. M., Hulscher, S. J. M. H., and Termes, A. P. P. (2009). “Modelling river dune evolution using a parameterization of flow separation.” J. Geophys. Res.: Earth Surf., 114(F1), F01014.
Paarlberg, A. J., Dohmen-Janssen, C. M., Hulscher, S. J. M. H., and Termes, P. (2007). “A parameterization of flow separation over subaqueous dunes.” Water Resour. Res., 43(12), W12417.
Paarlberg, A. J., Dohmen-Janssen, C. M., Hulscher, S. J. M. H., Termes, P., and Schielen, R. (2010). “Modelling the effect of time-dependent river dune evolution on bed roughness and stage.” Earth Surf. Processes Landforms, 35(15), 1854–1866.
Sekine, M., and Kikkawa, H. (1984). “Transportation mechanism of bed-load in an open channel.” Proc. Jpn. Soc. Civ. Eng., 351, 69–75 (in Japanese).
Sekine, M., and Kikkawa, H. (1992). “Mechanics of saltating grains II.” J. Hydraul. Eng., 536–558.
Shimizu, Y., Giri, S., Yamaguchi, I., and Nelson, J. (2009). “Numerical simulation of dune-flat bed transition and stage-discharge relationship with hysteresis effect.” Water Resour. Res., 45(4), W04429.
Simons, D. B., and Richardson, E. V. (1966). “Resistance to flow in alluvial channels.” U.S. Dept. of Interior, Washington, DC.
Smith, J. D., and McLean, S. R. (1977). “Spatially-averaged flow over a wavy surface.” J. Geophys. Res., 82(12), 1735–1746.
Tjerry, S., and Fredsøe, J. (2005). “Calculation of dune morphology.” J. Geophys. Res.: Earth Surf., 110(F4), F04013.
Tsujimoto, T., Mori, A., Okabe, T., and Ohmoto, T. (1990). “Non-equilibrium sediment transport: A generalized model.” J. Hydrosci. Hydraul. Eng., 7(2), 1–25.
Van den Berg, J., Sterlini, F., Hulscher, S. J. M. H., and van Damme, R. (2012). “Non-linear process based modeling of offshore sand waves.” Cont. Shelf Res., 37, 26–35.
Van Duin, O. J. M., Ribberink, J. S., Dohmen-Janssen, C. M., and Hulscher, S. J. M. H. (2012). “Particle step length variation along river dunes.” Proc., Int. Conf. on Fluvial Hydraulics, Taylor & Francis Group, London, 493–497.
Van Rijn, L. C. (1984). “Sediment transport. Part III: Bedforms and alluvial roughness.” J. Hydraul. Eng., 1733–1754.
Van Rijn, L. C. (1993). Principles of sediment transport in rivers, estuaries and coastal seas, AQUA, Amsterdam, Netherlands.
Venditti, J. G., Church, M., and Bennett, S. J. (2005a). “Morphodynamics of small-scale superimposed sand waves over migrating dune bed forms.” Water Resour. Res., 41(10), W10423.
Venditti, J. G., Church, M. A., and Bennett, S. J. (2005b). “Bedform initiation from a flat sand bed.” J. Geophys. Res., 110(F1), F01009.
Vidal, J.-P., Moisan, S., Faure, J.-B., and Dartus, D. (2007). “River model calibration, from guidelines to operational support tools.” Environ. Modell. Software, 22(11), 1628–1640.
Wilbers, A. W. E., and Ten Brinke, W. B. M. (2003). “The response of subaqueous dunes to floods in sand and gravel bed reaches of the Dutch Rhine.” Sedimentology, 50(6), 1013–1034.
Wong, M., and Parker, G. (2006). “Reanalysis and correction of bed-load relation of Meyer-Peter and Müller using their own database.” J. Hydraul. Eng., 1159–1168.
Yalin, M. S. (1964). “Geometrical properties of sand waves.” J. Hydraul. Div., 90(5), 105–119.
Yamaguchi, S., and Izumi, N. (2002). “Weakly nonlinear stability analysis of dune formation.” Proc., River Flow 2002, Swets and Zeitlinger, Lisse, Netherlands, 843–850.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 143 • Issue 2 • February 2017
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Oct 24, 2013
Accepted: Aug 3, 2016
Published online: Sep 30, 2016
Published in print: Feb 1, 2017
Discussion open until: Feb 28, 2017
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.