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 obtaine d from the digitization of multiple-image photographs. The mean angle of ejection is found to be about 30-degrees from the horizontal (rathe r than 90-degrees) with mean vertical ejection velocity of about 2u, where u is the friction velocity. Trajectories of saltating grains ha ve been computed, using the measurements of the initial ejection veloc ities and the mean velocity profile of the air flow. The results large ly agree with our measurements, and those of others, of mean values of maximum rise height, and the angles and velocities of particles at im pact with the bed, including measurements of saltating snow particles. The velocity results are correlated with u, the friction velocity. A n 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 t he large horizontal mean velocity acts to increase the vertical compon ent 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 v ertical 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 he ight and the vertical profiles of streamwise fluxes f1(z) and concentr ations of sand grains over a flat bed. It was found that above the thr eshold wind speed f1(z) is-proportional-to exp (-lambdagz/u2), Where the coefficient lambda varies over about 50%. The rapid increase in [v 1] above the mean height of the particles, and the exponential decreas e with height of the computed flux profile both agree with several set s of measurements in wind tunnels and in the field (collated here for the first time). However, unanswered questions about saltation still r emain. A model equation is proposed connecting the integrated horizont al flux F1(z) = integral-infinity/0 f1(z) dz, the vertical upwards flu x f3E and the average length l of trajectories. This suggests a signif icant correlation between l and f3E.