Wind tunnel modeling and measurements of the flux of wind-blown sand

This paper presents a way to empirically fit experimental data for the horizontal flux of various sizes of wind-blown dry sand using data from wind tunnel experiments. We measured vertical wind profiles to derive threshold shear velocity and estimated shear velocity and the flux of sand mass as a function of the height for nine different grain sizes. We propose a fitting model based on the experimental data and a least-squares method and derive an explicit form of sand flux as a function of height and shear velocity for these grain sizes. We also obtained an explicit form of the empirical equation for the measurement of sand transport per unit width and unit time by integrating the empirical equation as a function of height. Finally, we compared the effectiveness of Bagnold's equation, Kawamura's expression and Lettau and Lettau's equation, for predicting sand transport with the results of our empirical equation. The results show that the transport predicted by all of the equations were always lower than the measured results from the empirical equation for all grain sizes and shear velocities. However, the empirical equation matched Bagnold's equation, Kawamura's equation, and Lettau and Lettau's equation if the coefficients in these equations were adjusted instead of using their original coefficients. The empirical equation for sand transport in the present study contradicts previous conclusions generated by Bagnold's equation, which predict that for a given wind drag, the transport of a coarse sand is greater than that of a fine sand.