Saltation and incipient suspension above a flat particle bed below a turbulent boundary layer

Abstract

Experiments were conducted in a wind tunnel in which a turbulent boundary layer was naturally grown over flat beds of three types of nearly mono-disperse spherical particles with different diameters, densities and coefficient of restitution (r) (snow, 0.48 mm, 910 kg m−3; mustard seeds, 1.82 mm, 1670 kg m−3, r = 0.7; ice particles, 2.80 mm, 910 kg m−3, r = 0.8–0.9). The surface wind speeds (defined by the friction velocity u∗) were varied between 1.0 and 1.9 times the threshold surface wind speed (defined by u∗t). The trajectories, and ejection and impact velocities of the particles were recorded and analysed, even those that were raised only about one diameter into the flow.Measurements of the average horizontal flux of saltating particles per unit area, f(z), at each level z above the surface showed that, for u∗/u∗t [les ] 1.5, f(z) is approximately independent of the particle density and decreases exponentially over a vertical scale length lf, that is about 3 to 4 times the estimated mean height of the particle trajectories 〈h〉. Numerical simulations of saltating grains were computed using the measured probabilities of ejection velocities and the mean velocity profile of the air flow, but neglecting the direct effect of the turbulence. The calculated mean values of the impact velocities and the trajectory dimensions were found to agree with the measurements in the saltation range, where u∗/u∗t < 1.5. Similarly, in this range the simulations of the horizontal flux profile and integral are also consistent with the measurements and with Bagnold's u∗3 formula, respectively.When u∗/u∗t [ges ] 1.5, and u∗/VT [ges ] 1/10, where VT is the settling velocity, a transition from saltation to suspension occurs. This is indicated by the change in the mean mass flux profile which effectively becomes uniform with height (z) up to the top of the boundary layer. An explanation is provided for this low value of turbulence at transition relative to the settling velocity in terms of the random motion of the particles under the action of the turbulence when they reach the tops of their parabolic trajectories. The experiments show that, as u∗/u∗t increases from 1.0 to 1.9 the normalized mean vertical impact velocity 〈V3I〉/u∗ decreases by nearly 60% to about 0.6, which is less than 50% of the value for fluid particles. There is also a decrease in the vertical and horizontal component of the ejection velocity to values of 0.8 and 2.3, which are much less than their values in the saltation regime. We hypothesize that at the transition from saltation to suspension the ejection process changes quite sharply from being determined by impact collisions to being the result of aerodynamic lift forces and upward eddy motions.