Aeolian saltation: median height, mean grain size, and dimensionless shear velocity

We present field data demonstrating relationships associated with the development of aeolian mass flux profiles. Trajectories of saltating grains increase in height and length as their coefficient of restitution increases, thus do median saltation heights, h_s50. The coefficient depends, in part, on the momentum of a saltating grain relative to the inertia of the bed material that it impinges upon. This manifests in the smaller grains in a population bouncing higher off of a given surface than the coarser grains in that same population, as first described by Bagnold (1937), and more recently by Dong et al. (2004) and Namikas (2006), among others. More controversial has been the relationship between median saltation height and shear velocity, u_*, with some arguing that h_s50 increases with u_* (e.g., Bagnold, 1941; Owen, 1964; Willetts and Rice, 1985; Rice et al., 1995; Dong et al., 2012). Field investigations, however, have shown that h_s50 is insensitive to u_* (e.g., Creyssels et al., 2009; Ho et al., 2012; Martin and Kok, 2017; Delorme et al., 2023). These, and related studies, motivate this research.

Measurements were made at three sites in the Mojave/Sonoran Deserts of Southern California (CA sites) and three sites in the Jericoacoara National Park in Ceará, Brazil (BR sites). Sites were chosen to represent a range of grain sizes. At each site, the data-gathering protocols were similar. Flux profile data were obtained using vertical stacks of mesh traps, grain size statistics were obtained from the trapped sand, and shear velocities were estimated using 3-D ultrasonic anemometer measurements. Mean grain sizes, d₅₀, at CA1, CA2, and CA3 were 0.17, 0.18, and 0.16 mm. The respective values at BR1, BR2, and BR3 were 0.22, 0.39, and 0.39 mm. A total of 63 flux profiles and related data were evaluated.

Regression analysis was used to test for a dependence of h_s50 on a dimensionless shear velocity (u_* /u_*t, where the latter is the threshold shear velocity, estimated with d₅₀) and indicated a strong, inverse relationship (R² = 62%, P < 0.0001). When h_s50 is normalized by dividing by d₅₀, and the regression repeated, a statistically significant relationship was found. Finally, we tested for a relationship between the simple variables of median saltation height and mean grain size, finding that h_s50 increases with d₅₀ (R² = 53%, P < 0.0001). In summary, median saltation height is not dependent on shear velocity but does depend on mean grain size.