Partitioning resistance to overland flow on rough mobile beds

For overland flows transporting predominantly bed load over rough mobile beds without rainfall, resistance to flow f may be divided into four components: surface resistance f(s), form resistance f(f), wave resistance f(w), and bed-mobility resistance f(m). In this study it is assumed that f=f(s)+f(f)+f(w)+f(m), and an equation is developed for each component. The equations for f(s) and f(f) are borrowed from the literature, while those for f(w) and f(m) are developed from two series of flume experiments in which the beds are covered with various concentrations of large-scale roughness elements. The first series consists of 65 experiments on fixed beds, while the second series contains 194 experiments on mobile beds. All experiments were performed on the same slope (S = 0.114) and with the same size of sediment (D = 0.00074 m). The equations for f(w) and f(m) are derived by a combination of dimensional analysis and regression analysis. The analyses reveal that the major controls of f(w) and f(m) are the Froude number F and the concentration of the roughness elements C-r. When the equations for f(w) and f(m) are summed, the C-r terms cancel out, leaving f(w+m) = 0.63F(-2). An equation is developed that predicts total f(w) and the contributions of f(s), f(f), f(w) and f(m) to f are computed from the series 1 and 2 experiments. An analysis of the first series reveals that in clear-water flows over fixed beds, f(w) accounts for 52 per cent off. A similar analysis of the second series indicates that in sediment-laden flows over mobile beds f. comprises 37 per cent and f. 32 per cent off, so that together f. and f. account for almost 70 per cent of f. Finally, regression analyses indicate that where F > 0.5, f(w) and f(m) each vary with F-2 and f(w)/f(m) = 1.18. The equation developed here for predicting total f applies only to the range of hydraulic, sediment, and bed roughness conditions represented by the experimental data. With additional data from a broader range of conditions the same methodology as employed here could be used to develop a more general equation. Copyright (c) 2006 John Wiley & Sons, Ltd.