TR(BR)-9/98-99 : Mathematical modelling of branched flows in alluvial channels

Abstract

Branched flows in open channels with alluvial conditions occur in natural and man-made systems. Analysis of such flows by mathematical modelling is important considering its applications in water resources and environmental engineering. In this report a detailed review of existing models for flows in alluvial streams is presented. Models may be categorized based on (i) equations used, (ii) numerical method applied, in) consideration of physical processes. The governing equations for water flow and `moment flow are presented. The equations to be satisfied at junctions are also presented. Solution strategies and their variations are discussed. Various numerical methods for the solution of the governing equations are mentioned. Implementation of the boundary conditions is also described. A large number of existing computer codes to study flows in alluvial streams is presented. Performance of various models is problem dependent and no model is suitable for all types of problems. This is due to the poor understanding of the relation between flow and sediment transport. Thus, there is a scope to find the exact mechanism of sediment transport, which can be a potent area for future research. In addition, the roughness characteristics of the channel bed should also be estimated in the presence of sediment transport. Finally, a numerical scheme based on one-dimensional equations, a quasi-steady assumption and an uncoupled approach using explicit finite-difference method, is proposed. Although the model is expected to perform with greater efficiency and robustness, it is yet to be tested against measured data and needs further study.