Simulating Transient Sediment Waves in Aggraded Alluvial Channels by Double-Decomposition Method

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 M number of components, where M 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 R 2 ¼ 0:95. 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.

Numerical and Experimental Studies in Prediction of Bed Levels of Aggrading Channels

“…Singh 34,41 Tayfur and Singh 41 developed a 1D numerical model for prediction of bed levels due to aggradation process using Lax explicit finite difference scheme that use kinematic wave routing. The friction slope, suspended sediment concentration, particle velocity and particle fall (terminal) velocity were estimated using Chezy's equation, Velikanov 64 , Bridge and Dominic 65 , and Dietrich 66 respectively.…”

“…The parameters of sediment transport in overland flow (sheet sediment transport as suggested by Foster 33 ) were used in the simulation of laboratory data of Yen et al 32 . Tayfur and Singh 34 developed a mathematical model based on double decomposition method developed by Adomian 35,36 for simulation of aggrading bed and water surface profiles, and solved diffusive partial differential equations proposed by de Vries 3 . The method is simple and straightforward; however, its solution does not consider the transport of suspended and bed loads under non-equilibrium transport processes.…”

“…The estimated bed level variations from the proposed numerical scheme with different sediment transport functions are compared with actual observed data collected in the present study and reported from Soni et al 5 . The numerical model developed in this study, with best sediment transport function, for aggrading bed channels is also compared with numerical models developed in the previous studies 34,37,41 on prediction of bed and water levels of aggrading channels with uniform sediments.…”

Experimental Analysis of Sediment Deposition Due to the Effect of an Upstream Reservoir Backwater

“…Analytical and experimental approaches had been adopted to predict these elements due to aggradation occurrence. The experimental work under mobile bed condition is very limited compared to the analytical or mathematical approach [4][5][6][7][8]. Grade and Raju [2] mentioned that Sugioin (1962) was the first one to study the aggradation in laboratory flume and analyzed the data using dimensional analysis method.…”

“…Most of previous studies conducted experiment in the laboratory under idealized conditions of a prismatic channel carrying a constant discharge and sediment load. Analytical or mathematical solutions for simulating transient bed profile were also suggested by Tayfur and Singh [7,8], Soni [10,11], Ribberink and Vandersand [12], Parker et al [13] and Wu et al [14]. The experimental works on the aggradation phenomenon upstream reservoirs are very limited and, for this reason, this study had been conducted.…”