Discrete Particle Model for Analyzing Bedform Development
Publication: Journal of Hydraulic Engineering
Volume 128, Issue 4
Abstract
A discrete element model is used to simulate the emergence and evolution in time of wind ripples with the use of simple rules for the motion of individual sediment particles. It is shown, by analyzing the probabilities for the particles to be entrained and deposited over the bed implied by the selected rules, that the same model can be used to simulate the development of underwater bedforms. The results of the model show that the particle-transport processes implied by the simple rules used in the model can represent many different complex aspects of the physics of bedforms. The results of the model are compared with experimental results on underwater ripples obtained by the authors, and a surprisingly good agreement is found in terms of the main dynamical properties of the bedforms, such as growth rate of the amplitude, evolution of the steepness, growth saturation, and bedform celerity. Even though the simulated bedforms do not reproduce the exact geometry of their physical counterparts, the richness of the strongly nonlinear processes that this simple model is able to simulate makes this kind of approach useful to explain many of the observed features of underwater bedforms, which are otherwise very difficult to address theoretically.
Get full access to this article
View all available purchase options and get full access to this article.
References
Aracena, D. (1999). “Experimental study on bedforms in heterogeneous sediment beds.” Undergraduate thesis. Dept. of Civil Engineering, Univ. of Chile (in Spanish).
Bagnold, R. A. (1941). The physics of blown sand and desert dunes, Chapman and Hall, London.
Barahona, M. (1997). “Experimental study on the interaction between a turbulent flow and a granular movable bed.” Undergraduate thesis. Dept. of Civil Engineering, Univ. of Chile (in Spanish).
Coleman, S., and Melville, B.(1994). “Bedform development.” J. Hydraul. Eng., 120(5), 544–560.
Coleman, S., and Melville, B.(1996). “Initiation of bedforms on a flat sand bed.” J. Hydraul. Eng., 122(6), 301–310.
Einstein, H. A. (1950). “The bedload function for sediment transportation in open channel flow.” U.S. Dept. Agric., Tech. Bull., No. 1026. U.S. Dept. Agriculture, Washington, D.C.
Engelund, F.(1970). “Instability of erodible beds.” J. Fluid Mech., 42(2), 225–244.
Exner, F.(1925). “Uber die Wechselwirkung Zwischen Wasser und Geschiebe.” Flüssen, Sitzber. Akad. Wiss. Wien, pt. IIa, Bd. 134, pp. 199.
Fredsøe, J.(1974). “On the development of dunes in erodible channels.” J. Fluid Mech., 64(1), 1–16.
Fredsøe, J.(1982). “Shape and dimensions of stationary dunes in rivers.” J. Hydraul. Div., Am. Soc. Civ. Eng., 108(HY8), 932–947.
Grinvald, D. I., and Nikora, V. I. (1988). “River turbulence.” Hydrometeoizdat, Leningrad, Russia.
Ji, Z., and Mendoza, C.(1997). “Weakly nonlinear stability analysis for dune formation.” J. Hydraul. Eng., 123(11), 979–985.
Landry, W., and Werner, B. T.(1994). “Computer simulations of self-organized wind ripple patterns.” Physica D, 77, 238–260.
Meyer-Peter, E., and Muller, R. (1948). “Formulas for bedload transport.” Proc., 2nd Int. Association for Hydraulic Research Congress, Stockholm, Sweden.
Nelson, J., McLean, S. R., and Wolfe, S. R.(1993). “Mean flow and turbulence fields over two-dimensional bedforms.” Water Resour. Res., 29(12), 3935–3953.
Nelson, J. M., Schmeeckle, M. W., Shreve, R. L., and McLean, S. R. (2000). “Sediment entrainment and transport in complex flows.” Selected Papers of the Int. Association for Hydraulic Research Symposium on River, Coastal and Estuarine Morphodynamics, Genova, Italy.
Nikora, V. I., and Hicks, D. M.(1997). “Scaling relationships for sand wave development in unidirectional flow.” J. Hydraul. Eng., 123(12), 1152–1156.
Niño, Y., and Atala, A.(1999). “Discrete computer simulation of bedforms.” Mech. Res. Commun., 26(1), 91–98.
Niño, Y., and Barahona, M., “Laboratory observations on sediment-turbulence interactions over bedforms.” J. Eng. Mech., in press.
Niño, Y., Garca, M., and Ayala, L.(1994). “Gravel saltation 1: Experiments.” Water Resour. Res., 30(6), 1907–1914.
Niño, Y., and Garca, M.(1998). “Experiments on saltation of sand in water.” J. Hydraul. Eng., 124(10), 1014–1025.
Nishimori, H., and Ouchi, N.(1993). “Formation of ripple patterns and dunes by wind-blown sand.” Phys. Rev. Lett., 71(1), 197–200.
Raudkivi, A. J.(1966). “Bedforms in alluvial channels.” J. Fluid Mech., 26, 507–514.
Sharp, R. P.(1963). “Wind ripples.” J. Geol., 71, 617–636.
Smith, J. D.(1970). “Stability of sand bed subject to a shear flow of low Froude number.” J. Geophys. Res., 75(30), 5928–5940.
Werner, B. T., Haff, P. K., Livi, R. P., and Anderson, R. S.(1986). “Measurement of eolian ripple cross-sectional shapes.” Geol. J., 14, 743–745.
Williams, P. B., and Kemp, P. H.(1971). “Initiation of ripples on flat sediment beds.” J. Hydraul. Div., Am. Soc. Civ. Eng., 97(HY8), 505–522.
Williams, P. B., and Kemp, P. H.(1972). “Initiation of ripples by artificial disturbances.” J. Hydraul. Div., Am. Soc. Civ. Eng., 98(HY8), 1057–1070.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 128 • Issue 4 • April 2002
Pages: 381 - 389
Copyright
Copyright © 2002 American Society of Civil Engineers.
History
Received: Mar 7, 2001
Accepted: Aug 23, 2001
Published online: Apr 1, 2002
Published in print: Apr 2002
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.