Farrell, E.J. and Sherman, D.J., 2013. Estimates of the Schmidt Number for vertical flux distributions of wind-blown sand. In: Conley, D.C., Masselink, G., Russell, P.E. and O'Hare, T.J. (eds.)

From studies of suspended sediments in water or dust in air it is recognized that the Rouse profile represents a theoretically sound, first approximation of characteristic sediment concentration gradients. Rouse (1938) combined the influence of grain size and shear velocity changes into a universal equation. The Rouse number relates sediment size (in the form of settling velocity, w₀) to shear velocity, the von Kármán constant (0.4) and the Schmidt Number, typically assumed to be equal to 1.0 but with much larger values reported. The shape of the Rouse concentration profile is controlled by the Rouse number exponent. We applied the Rouse profile model to 14 vertical flux profiles of wind-blown sand measured during a field experiment in Jericoacoara, Brazil in 2008. These data were supplemented with 96 vertical flux profiles obtained from fourteen wind tunnel and field experiments reported in the literature, for a total of 110 profiles. The analyses show that the performance of the Rouse model is not sensitive to changes in the range of variability we can expect to observe in values of fall velocity, shear velocity and the von Kármán constant but is very sensitive to changes in the values of the Schmidt number. First, the Rouse model was applied to vertical flux profiles using the common Schmidt number value of 1.0 in the Rouse number exponent. The model performed poorly in predicting the shape and magnitude of the vertical flux distributions (38% and 18% of the observed transport rate in field and wind tunnels, respectively). Alternative values were derived by adapting the profiles to equivalent concentration Rouse-type ratios and obtaining the slope values of the fitted power functions. With this approach, in field and wind tunnel experiments, the values of the Schmidt number ranged from 4.46 - 19.10 and 0.68 - 23.24, respectively, and predicted, on average, 82% and 90% of the observed transport rate. We tested a third method that does not require measuring vertical flux profiles. We found a strong relationship between the Schmidt number and a shear velocity - fall velocity ratio (r²= 0.65), with values ranging from 6.11 – 14.80 and 0.86 – 17.83, for field and wind tunnel experiments, respectively. These modified values of the Rouse exponents also resulted in vertical profiles that predicted similar distributions to the observed flux data and provide good predictions of the total transport rates (86% and 81% in field and wind tunnels experiments, respectively). To our knowledge, these are the first values of the Schmidt number derived for aeolian sand transport and the first successful application of the Rouse model to vertical flux profiles of saltation.