Stratification effects in sediment-laden air flow
1, Douglas Sherman2
1Xi'an Jiaotong-Liverpool University, Suzhou, Jiangsu, China, 2University of Alabama, Tuscaloosa, AL, USA
Many laboratory studies have shown that velocity profiles in sediment-laden water deviate from the expected log-linear relationship. One common explanation for this phenomenon is that it results from flow stratification induced by a sediment concentration gradient. This stratification effect damps the development of turbulence and changes the structure of eddies. The process is often analogized to temperature-induced stratification in a stable atmosphere (Stull, 1976), which is often quantified by a form of Richardson number.
In sediment-laden flow, the modified velocity profiles should still obey the Law of the Wall, however, a correction parameter, Φm, is necessary:
where u is the streamwise velocity at elevation of z, u* is the shear velocity, k is the von Karman constant (about 0.4). The correction parameter is a function of flux, Rf, or, gradient, Ri, Richardson number:
where α and β are constants. Note α is the Schmidt number, representing the ratio of eddy viscosity to eddy diffusivity, commonly assumed to approximate 1. In thermally stable flow, Ri and Rf are greater than a critical value of 0.25 (Stull, 1976).
We developed depth-averaged, sedimentological gradient and flux Richardson numbers (Ria and Rfa, respectively) to evaluate potential stratification effect in sand-laden air flow. We conducted 15 runs of experiments near Jericoacoara, Ceará, Brazil. Detailed description of the field site and experimental design experiment are documented in Li et al. (2010). Our results indicate that Ria ranges from 0.50 to 10.43, and Rfa from 1.11 to 10.64: both ranges well above the critical value of 0.25, and indicating that the flow is stably stratified. The Schimdt numbers ranged from 1.15 to 2.75,. These values were less than those (4.46-11.90) found by Farrell and Sherman (2013), but within the range (0.1-10) reported from many experiments conducted in water (Lees, 1981; Farber, 1986). We found values of β from 0.012 to 0.100, which were much less than those (4.0-10.0) of hydrodynamic studies (e.g., Gelfenbaum and Smith,1986; Herrmann and Madsen, 2007).
This study explored the stratification effect on the streamwise velocity profile caused by saltation-flux gradients in sand-laden air flow, and quantified those effects using a pair of sedimentological Richardson numbers (flux and gradient). This study derived a range of estimates for the Schmidt number and the constant β. These results can help us better understand sand-air interactions, and improve our ability to represent sand flux and wind velocity gradients near the surface.