Numerical analysis of adaptation-to-capacity length for fluvial sediment transport

Over the last several decades, various sediment transport capacity formulations have been used by geomorphologists and engineers to calculate fluvial morphological changes. However, it remains poorly understood if the adaptation to capacity could be fulfilled instantly in response to differing inflow discharges and sediment supplies, and thus if the calculation of morphological changes in rivers based on the assumed capacity status is fully justified. Here we present a numerical investigation on this issue. The distance required for sediment transport to adapt to capacity (i.e., adaptation-to-capacity length) of both bed load and suspended sediment transport is computationally studied using a coupled shallow water hydrodynamic model, in line with varied inlet sediment concentrations. It is found that the adaptation-to-capacity length generally decreases as the Rouse number increases, irrespective of whether the inlet sediment concentration increases or reduces. For cases with vanishing inlet sediment concentration, a unified relationship is found between the adaptation-to-capacity length and the Rouse number. Quantitatively, the adaptation-to-capacity length of bed load sediment is limited to tens of times of the flow depth, whilst that of suspended sediment increases substantially with decreasing Rouse number and can be up to hundreds of times of the flow depth. The present finding concurs that bed load sediment transport can adapt to capacity much more rapidly than suspended sediment transport, and it facilitates a quantitative criterion on which the applicability of bed load or suspended sediment transport capacity for natural rivers can be readily assessed.