Closure to “ Numerical Simulation of Degradation of Alluvial Channel Beds ” by Inbo Park and Subhash C. Jain (July, 1987, Vol. 113, No. 7)

Abstract

Discussion by Jinn-Chuang Yang 3 Numerical modeling of sediment transport in alluvial channels has been extensively studied for the past decade. A number of models have been developed for the corresponding specific problems. However, as the authors pointed out, most of the papers do not discuss the effect of At and Ax on the simulation results. Based on the bed-perturbation celerity relation proposed by de Vries and the use of a simple sediment-transport predictor, the authors have derived Eqs. 21 and 24 for determining the most appropriate At and Ax to avoid the numerical instability. Nevertheless, as far as the nonuniform sediment transport is concerned, the bed perturbation is induced not only by the bed-level change but also by the variation of the composition of bed material. In view of Eqs. 21 and 24, the time and space steps At and Ax are related to the Froude number, mean flow velocity, and sediment concentration. It is obvious that the perturbation caused by the nonuniformity of the bed material is not considered. Therefore, strictly speaking, Eqs. 21 and 24 should only be valid for the uniform sand transport model. In addition, the relations derived are based on the simple power law relation, Eq. 20, for a sediment discharge predictor, which is not consistent with Eq. 4. Therefore, the use of Eqs. 21 and 24 may give the wrong indication of A? and Ax selection. The necessity of appropriately selecting At and Ax is resulted from the explicit scheme used by the authors for the sediment continuity equation. One can probably use the implicit scheme such as Preissmann's four-point scheme, which is unconditionally stable, to avoid the Courant-number constraint. Although the existence of multiple time (or length) scales may lead to an instability problem, with the careful choice of space weighting factor one need not worry about the instability caused by an unsuitable choice of Af and Ax (24).