Simulating Transient Sediment Waves in Aggraded Alluvial Channels by Double-Decomposition Method
Publication: Journal of Hydrologic Engineering
Volume 16, Issue 4
Abstract
By using the double-decomposition (DD) method, this study simulates transient sediment waves caused by aggradation described by a diffusion-type partial differential equation (PDE). The DD method solves the PDE by decomposing the solution function for sediment rate into a summation of number of components, where stands for the order of approximation. The solution was approximated by considering only the first three terms. The model satisfactorily simulated laboratory-measured aggradation bed profiles with, on average, a mean absolute error (MAE) of 0.70 cm, a root-mean-square error (RMSE) of 0.84 cm, a mean relative error (MRE) of 1.11%, and . The model performance was also tested by using numerical and error-function solutions. In addition, the results obtained from application of the DD solution to hypothetical field cases were found to be theoretically compatible with what may be observed in natural streams. However, sediment wave fronts in later periods of the simulation time reached equilibrium bed levels more quickly, around in the middle section of the channel.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This research was supported by the Scientific and Technological Research Council of Turkey [TUBITAK] under Grant No. UNSPECIFIED106M274. The writers extend their sincere appreciation to TUBITAK for the financial support. The writers would also like to express their thanks to Professor Engin Aktas of the Civil Engineering Dept., Izmir Institute of Technology; and Professor Oguz Yilmaz of the Dept. of Mathematics, Izmir Institute of Technology for valuable discussions.
References
Adomian, G. (1984). “A new approach to nonlinear partial differential equations.” J. Math. Anal. Appl., 102, 420–434.
Adomian, G. (1988). “A review of decomposition method in applied mathematics.” J. Math. Anal. Appl., 135, 501–544.
Aricò, C., and Tucciarelli, T. (2008). “Diffusive modelling of aggradation and degradation in artificial channels.” J. Hydraul. Eng., 134(8), 1079–1088.
Bor, A. (2009). “Numerical modelling of unsteady and non-equilibrium sediment transport in rivers.” M.Sc. thesis, Izmir Institute of Technology, Turkey.
Bridge, J. S., and Dominic, D. F. (1984). “Bed load grain velocities and sediment transport rates.” Water Resour. Res., 20(4), 476–490.
de Vries, M. (1965). “Consideration about non-steady bed-load transport in open channels.” Proc. XI Congress, IAHR, Delft, the Netherlands, 3, paper 3.8.
de Vries, M. (1973). “River bed variation—Aggradation and degradation.” Int. Seminar on Hydraulics of Alluvial Streams, IAHR, Delft, the Netherlands (also available as Delft Hydraulic Laboratory, Delft, 1973, Pub. No. 107).
Dietrich, C. R., Green, T. R., and Jakeman, A. J. (1999). “An analytical model for sediment transport: Application to Murrey and Murrunbridge river reaches, Australia.” Hydrol. Processes, 13(5), 763–776.
Dietrich, W. E. (1982). “Settling velocity of natural particles.” Water Resour. Res., 18(6), 1615–1626.
Guy, H. P., Simons, D. B., and Richardson, E. V. (1966). “Summary of alluvial channel data from flume experiments, 1956–1961.” Professional Paper, 462-I, U.S. Geological Survey 96.
Langbein, W. B, and Leopold, L. B. (1968). “River channel bars and dunes—Theory of kinematic waves.” Professional Paper, 422-L,, U.S. Geological Survey 20.
Lisle, T. E., Cui, Y. T., Parker, G., Pizzuto, J. E., and Dodd, A. M. (2001). “The dominance of dispersion in the evolution of bed material waves in gravel-bed rivers.” Earth Surf. Processes Landforms, 26, 1409–1420.
Lisle, T. E., Pizzuto, J. E., Ikeda, H., Iseya, F., and Kodama, Y. (1997). “Evolution of a sediment wave in an experimental channel.” Water Resour. Res., 33, 1971–1981.
Pianese, D. (1994). “Comparison of different mathematical models for river dynamics analysis.” Int. Workshop on Floods and Inundations Related to Large Earth Movements. Ministry of Public Works, Rome, paper no. 782, 24.
Shan, Y. X., and Hong, W. O. W. (2001). “The analytical solution for sediment reaction and diffusion equation with generalized initial boundary conditions.” Appl. Math. Mech., 22(4), 404–408.
Singh, A. K., Kothyari, U. C., and Raju, K. G. R. (2004). “Rapidly varying transient flows in alluvial rivers.” J. Hydraul. Res., 42(5), 473–486.
Soni, J. P. (1975). “Aggradation in streams due to increase in sediment load.” Ph.D. thesis, Univ. of Roorkee, Roorkee, India.
Soni, J. P. (1981a). “An error function solution of sediment transport in aggradation channels.” J. Hydrol. (Amsterdam), 49, 107–119.
Soni, J. P. (1981b). “Unsteady sediment transport law and prediction of aggradation parameters.” Water Resour. Res., 17(1), 33–40.
Tayfur, G., and Singh, V. P. (2006). “Kinematic wave model of bed profiles in alluvial channels.” Water Resour. Res., 42(6), W06414.
Tayfur, G., and Singh, V. P. (2007). “Kinematic wave model for transient bed profiles in alluvial channels under nonequilibrium conditions.” Water Resour. Res., 43, W12412.
Vasquez, J. A., Steffler, P. M., and Millar, R. G. (2008). “Modeling bed changes in meandering rivers using triangular finite elements.” J. Hydraul. Eng., 134(9), 1348–1352.
Velikanov, M. A. (1954). “Gravitational theory of sediment transport.” J. Sci. Soviet Union, Geophys., 4 (in Russian).
Vreugdenhil, C. B., and de Vries, M. (1973). “Analytical approaches to non-steady bedload transport.” Research Rep., S 78 part IV, Delft Hydraulic Laboratory, Delft, the Netherlands, 16.
Wathen, S. J., and Hoey, T. B. (1998). “Morphological controls on the downstream passage of a sediment wave in a gravel-bed stream.” Earth Surf. Processes Landforms, 23, 715–730.
Wu, W. (2004). “Depth-averaged two-dimensional numerical modelling of unsteady flow and nonuniform sediment transport in open channels.” J. Hydraul. Eng., 130(10), 1013–1024.
Wu, W., Vieira, D. A., and Wang, S. S. Y. (2004). “One-dimensional numerical model for nonuniform sediment transport under unsteady flows in channel networks.” J. Hydraul. Eng., 130(9), 914–923.
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 16 • Issue 4 • April 2011
Pages: 362 - 370
Copyright
© 2011 American Society of Civil Engineers.
History
Received: Oct 2, 2009
Accepted: Sep 23, 2010
Published online: Sep 27, 2010
Published in print: Apr 1, 2011
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.