Abstract
Bed forms of various kinds that evolve naturally on the bottom of sandy coasts and rivers are a result of the kinematics of bed load transport. Based on the group motion of particles in the bed load within the bottom layer, a study on the nonlinear dynamics of bed load transport is presented in this paper. It is found that some development stages, such as the initiation, the equilibrium sediment transport, and the transition from a smooth bed to sand dunes, can be accounted for by different states in the nonlinear system of the bed load transport. It is verified by comparison with experimental data reported by Laboratoire Nationae D’Hydraulique, Chatou, France, that the evolution from a smooth bed to sand dunes is determined by mutation in the bed load transport. This paper presents results that may offer theoretical explanations to the experimental observations. It is also an attempt to apply the state-of-the-art nonlinear science to the classical sediment transport mechanics.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Hao B L. Publish Illustration to Nonlinear Science Series «Nonlinear Science Series» (in Chinese). Shanghai: Shanghai Science Education Press, 1992
Lin Z S. Nonlinear Science and its Application in the Geo-science (in Chinese). Beijing: Meteorological Press, 2003
Qian N, Wan Z H. Kinematical Mechanics of Sediment (in Chinese), Beijing: Science Press, 2003
Einstein H A. The Bed Load Function for Sediment Transportation in Open Channel Flows. US Dept Agri, Tech Bull, 1026, 1950, 71
Han Q W, He M M. Statistic Theory of Sediment Movement (in Chinese). Beijing: Science Press, 1984
Bai Y C, Andreas M A, Jiang C B. A linear theory for disturbance of coherent structure and mechanism of sand wave in open channel flow. International Journal of Sediment Research, 2001, 15(2): 234–243
Bai Y C, Luo J S. The loss of stability of laminar flow in open channel and the mechanism of sand ripple formation. Appl Math Mech, 2002, 23(3): 254–268
Bai Y C, Jiang C B, Luo J S, et al. Coherent structure of the bottom layer in the oscillating flow and its interaction with the sediment. Advances in Mechanics (in Chinese), 2003, 33(3): 347–356
Bai Y C, Xu H J. A study on the stability of laminar open-channel flow over a sandy rippled bed. Sci China Ser E-Eng Mater Sci, 2005, 35(1): 83–103
He W S, Cao S Y, Lei X Z, et al. Nonlinear theory on the initiation of the sediment. J Hydr Engin, 2004, (1): 28–32
Gessler J. Critical shear stress for sediment mixtures. Proc 14th Conf Intern Assoc Hydraulic Research, 1971, 3: 1–8
Einstein H A. The bed load function of sediment transportation in open channel flows. US Dept Agri, Tech Bull, 1026, 1950, 71
Coleman N L. A theoretical and experimental study of drag and lift forces acting on a sphere resting on hypothetical stream-bed, Proc 12th Cong Intern Assoc Hydraulic Research, 1967, 3: 78–90
Rowe P N, Henwood G A. Drag forces in a hydraulic model of a fluidized bed, part I. Tran Institute of Chem Engin, 1961, 39(1): 41–45
Albertson M L, Simons D B, Richardson E V. Discussion-Mechanics of Sediment Ripple Formation. In: Liu H K, ed. J Hydr Div Proc, Amer Soc Civil Engrs, 1958, 84(HY1)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bai, Y., Xu, H., Xu, D. et al. Nonlinear dynamical characteristics of bed load motion. SCI CHINA SER E 49, 365–384 (2006). https://doi.org/10.1007/s11431-006-0365-2
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s11431-006-0365-2