Abstract
Experiments were performed to analyse the interaction between a vortex ring and a sloped sediment layer. Attention focussed on interactions under “critical” conditions, in which sediment motion was only just induced by the ring's flow field. Both hydraulically smooth and hydraulically rough bedforms were analysed, using near-spherical monodisperse sediments with relative densities of 1.2 and 2.5 and mean diameters (dp) ranging between 80 and 1087 μm. Measurements of the vortex-ring flow field were obtained, during the interaction, using two-dimensional particle imaging velocimetry. The threshold conditions for incipient sediment motion were analysed in terms of the critical Shields parameter (Nc), defined in terms of the peak tangential velocity measured adjacent to the bed surface. Bed-slope effects were investigated by tilting the sediment layer at various angles between the horizontal and the repose limit for the sediment. In all cases, the propagation axis of the vortex ring was aligned normal to the bed surface. The measured values of Nc were compared with a force-balance model based on the conditions for incipient grain motion on a sloping bed. For hydraulically smooth bedforms, where the bed roughness is small compared to the boundary-layer depth, the model was derived to account for how viscous stresses affect the drag and lift forces acting on the near surface sediment. For hydraulically rough bedforms, where this viscous-damping effect is not present, the model assumes the drag and lift forces scale with the square of the near-bed (inviscid) velocity scale. In both cases, the model predicts that bedforms become more mobile as the bed slope is increased. However, the damping effect of the viscous sublayer acts as a stabilizing influence for hydraulically smooth bedforms, to reduce the rate at which the bed mobility increases with bed slope. The measured values of Nc were in agreement with the trends predicted by this model, and exhibit a transition in behaviour between the smooth-bed and rough-bed cases when dp/δs ≈ 20 (where δs is the viscous-sublayer length scale).
Highlights
Methods for predicting bedload sediment-transport rates are largely empirical, and based on measurements taken in steady turbulent channel flows
This paper extends the work of Munro et al.[10] and describes experiments to investigate how the flow-field of an isolated vortex ring, made to interact with a sediment layer, gives rise to incipient sediment motion
For a steady turbulent channel flow, estimation of the bed shear stress σ b is standard. [For example, σb√= ρu2∗, where u∗ is the bed shear velocity, which for a shallow-sloped channel is given by u∗ = g Rh S, where Rh and S denote the hydraulic radius and channel gradient, respectively.3] For the experiments described in this article, the boundary layer induced by the interaction evolves spatially and with time
Summary
Methods for predicting bedload sediment-transport rates are largely empirical, and based on measurements taken in steady turbulent channel flows. In such flows, the near-bed turbulent fluctuations, which give rise to the hydrodynamic drag and lift forces that induce sediment motion, are correlated with the time-averaged mean velocity. The integral parameter used in standard models is the time-averaged mean bed shear stress,[1,2,3,4] with the effects due to turbulent fluctuations considered implicitly.
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