Closed-conduit bed-form initiation and development

Nonintrusive measurement of closed-conduit erodible-bed development was undertaken for 12 experiments of ranges of flow strengths and sediment (solids) sizes. Analogous to open-channel flows, wavelets on the sediment bed of a closed-conduit are instigated by discontinuities in the bed, with wavelet lengths λ for laminar and turbulent open-channel and closed-conduit flows given by λ =175d⁰.⁷⁵, where λ and sediment size d are in millimeters. For closed-conduit flows, ripples, and dunes grow from these wavelets (at rates increasing with increasing flow strength, and utilizing the mechanisms of bed-form coalescence and throughpassing) to limiting lengths, heights, steepnesses, and bed friction factors that are approximately maintained or possibly decrease thereafter. Limitation of free-surface deformation results in increased rates of bed-wave development for closed-conduit flows in comparison to open-channel flows. Measured results indicate that equilibrium closed-conduit ripple and dune magnitudes can be predicted using relations derived for equivalent open-channel flows. The present findings are of particular relevance for understanding and modeling engineering activities ranging from dredging to transport of solids in stormwater and sewer systems, bed-form transport of solids in closed conduits influencing (potentially markedly) conduit conveyance, rate of solids transport, and system head losses for such flows.