Saltating motion of a bead in a rapid water stream

Abstract

This paper experimentally and numerically investigates the two-dimensional saltating motion of a single large particle in a shallow water stream down a steep rough bed. The experiment is prototypical of sediment transport on sloping beds. Similar to the earlier experimental results on fine particles entrained by a turbulent stream, we found that most features of the particle motion were controlled by a dimensionless shear stress (also called the Shields number) N(Sh) defined as the ratio of the bottom shear stress exerted by the water flow to the buoyant weight of the particle (scaled by its cross-sectional area to obtain a stress). We did not observe a clear transition from rest to motion, but on the contrary there was a fairly wide range of N(Sh) (typically 0.001-0.005 for gentle slopes) for which the particle could be set in motion or come to rest. When the particle was set in motion, it systematically began to roll. The rolling regime was marginal in that it occurred for a narrow range of N(Sh) (typically 0.005-0.01 for gentle slopes). For sufficiently high Shields numbers (N(Sh)>0.3), the particle was in saltation. The mean particle velocity was found to vary linearly with the square root of the bottom shear stress and here, surprisingly enough, was a decreasing function of the channel slope. We also performed numerical simulations based on Lagrangian equations of motion. A qualitative agreement was found between the experimental data and numerical simulations but, from a quantitative point of view, the relative deviation was sometimes substantial (as high as 50%). An explanation for the partial agreement is the significant modification in the water flow near the particle.

Sediment resuspension and erosion by vortex rings

“…When considering resuspension from a sediment layer, additional forces are involved due to interparticle collisions and cohesion. The upward ͑or streamwise͒ force resulting from the momentum transfer when two sediment grains collide scales as 10 p 0 d 2 , whereas cohesive forces are known to be significant for fine sediments only, 31 typically with d Շ 30 m, significantly smaller than the particles considered in this article. In the present context, therefore, we expect forces of the form F L and F B to remain the dominant terms in the force balance for resuspension.…”

“…[5][6][7][8][9][10][11] Using artificial micron-sized sediment ͑with relative density 1.05͒, Kaftori et al 7 showed particle transport, resuspension, and deposition to be largely controlled by the action of streamwise coherent wall structures identified as funnel-type vortices ͑i.e., taking the shape of an expanding spiral, wound around a funnel laid sideways in the direction of the flow͒. Further experiments, 9 with improved resolution of the fluid flow field and particle motions in the near-wall region, have extended this study to consider natural sediments.…”

The interaction of a vortex ring with a sloped sediment layer: Critical criteria for incipient grain motion

“…(12b), with Q /Q 0 = 1 assumed, is consistent with experimental data (using hydraulically rough bedforms). 19,20,37 In particular, Chiew and Parker, 20 using natural sediments with d p between 500 and 2700 μm and streamwise bed slopes in the range 0 ≤ β/β r ≤ 0.85, found good agreement with measurements of u * ,c /u * ,c,0 obtained from a steady closed-conduit flow, where the critical bed shear velocity (u * ,c ) was estimated using a standard empirical formulation based on the streamwise time-averaged mean flow velocity. Figure 10 shows the measured values ofû b,c /û b,c,0 plotted against β/β r , with each sediment type indicated by a different data symbol (see caption).…”

Periodic saltation over hydrodynamically rough beds: aeolian to aquatic

“…More references can be found in recent reviews on Aeolian transport (Durán et al 2011, Kok et al 2012, Valance et al 2015. Saltation may also be relevant in aquatic flows (Fernandez Luque & van Beek 1976, Abbot & Francis 1977, Ancey et al 2002, Niño & García 1998. The differences in saltation occur because of the difference in the mass density of the material of the grains relative to that of air and water and the differences in the kinematic viscosities of the two fluids.…”