SALTATING PARTICLES OVER FLAT BEDS

Measurements of ejection and impact velocities, trajectory lengths and maximum rise heights of sand grains (median diameters 118 and 188 mum) in saltation over a flat sand bed in a wind tunnel have been obtained from the digitization of multiple-image photographs. The mean angle of ejection is found to be about 30-degrees from the horizontal (rather than 90-degrees) with mean vertical ejection velocity of about 2u*, where u* is the friction velocity. Trajectories of saltating grains have been computed, using the measurements of the initial ejection velocities and the mean velocity profile of the air flow. The results largely agree with our measurements, and those of others, of mean values of maximum rise height, and the angles and velocities of particles at impact with the bed, including measurements of saltating snow particles. The velocity results are correlated with u*, the friction velocity. An essential point is that, even for particles as small as 100 mum, the fact that the drag law is nonlinear (i.e. non-Stokesian) means that the large horizontal mean velocity acts to increase the vertical component of drag on particles. This effect reduces the height to which they rise by 40% to 50% compared with the value in still air for a given vertical ejection velocity. Using the measured probability distribution of ejection velocities, an ensemble of trajectories was computed and thence the average horizontal velocity [v1] of particles at a given height and the vertical profiles of streamwise fluxes f1(z) and concentrations of sand grains over a flat bed. It was found that above the threshold wind speed f1(z) is-proportional-to exp (-lambdagz/u*2), Where the coefficient lambda varies over about 50%. The rapid increase in [v1] above the mean height of the particles, and the exponential decrease with height of the computed flux profile both agree with several sets of measurements in wind tunnels and in the field (collated here for the first time). However, unanswered questions about saltation still remain. A model equation is proposed connecting the integrated horizontal flux F1(z) = integral-infinity/0 f1(z) dz, the vertical upwards flux f3E and the average length l of trajectories. This suggests a significant correlation between l and f3E.