An experimental study of the dynamics of saltation within a three-dimensional framework
Introduction
The ballistic trajectories of wind-blown particles, known as saltation, are associated with a wide range of features observed on planetary surfaces, both erosional (e.g. ornamentation on ventifacts, desert pavements and yardangs) and depositional (e.g. sand sheets, impact ripples and dunes) in nature. In this geophysical process, momentum is transferred from the airflow to the bed, initiating a cascade of particle ejections and ricochets such that the cloud of saltators rapidly expands in height and breadth along the path of the mean airflow. At some finite distance downwind, the particle concentration reaches saturation and the fluid momentum flux is suggested to drop below the threshold for aerodynamic entrainment of particles resting on the bed surface (Owen, 1964). Ballistic impacts during saltation are widely recognized to drive the emission of dust and thereby affect air quality and contaminant transport on a global scale. Hence, the physics of saltation has been a primary area of investigation for over 75 years since the early seminal work of Bagnold (1941).
A large number of studies have addressed the vertical distribution of the horizontal flux, q(x), inclusive of Bagnold, 1941, Sharp, 1964, Williams, 1964, Nickling, 1978, Nickling, 1983, Anderson and Hallet, 1986, Nalpanis et al., 1993, Zou et al., 2001, and Wang et al. (2006). A consensus built upon empirically based wind tunnel and field studies, as well as computational models of the saltation cloud, suggests that a majority of particles travel within 1–2 cm of the bed surface, and that q decays exponentially with height (z) (Butterfield, 1999, Rasmussen and Sorensen, 2008). The full height of the saltation cloud observed in field settings generally exceeds that observed in the laboratory (Sharp, 1964).
Direct measurement of the vertical profile of the particle transport rate tends to be constrained by the dimensions of the instrumentation to a relatively coarse (cm) spatial resolution. Commonly used sensors include: i) either segmented or stacked sand traps (e.g. BSNE traps; Fryrear, 1986), ii) Peizoelectric sensors (Baas and Sherman, 2005, Sherman et al., 2011), iii) Sonic sensors (e.g. saltiphones; Cornelis et al., 2004), and particle counters (e.g. Wenglor gate sensors; Barchyn et al., 2014). None of these instruments provide information on the velocity components of the sampled particles to obtain the particle-borne momentum flux of the ascending and descending populations, although the amalgamated size distribution can be obtained by sieving the contents obtained from sediment traps. Such measurements are also lumped so that the departure of particle trajectories from the alignment of the mean wind is not isolated to provide information on the spanwise diffusion within the saltation cloud. As compared to the fetch effect associated with the particle cascade (Chepil, 1957, Gillette et al., 1996), the diffusion of particles moving normal to the mean airflow has received relatively little consideration except for only a few works involving high speed photography (Yang et al., 2009, O'Brien and McKenna Neuman, 2016), and a discrete particle 2.5D model (Kang, 2012). Indeed, O'Brien and McKenna Neuman (2016) were able to determine from their wind tunnel experiments that as little as 12% of all particles travel in ballistic trajectories that are strictly wind aligned, ±1°.
More advanced, laser based methods of measuring the wind aligned particle transport rate have been employed in wind tunnel simulations, though these technologies are costly and fragile. They include Laser Doppler Anemometry (Li and McKenna Neuman, 2014), Particle Imaging Velocimetry (Yang et al., 2007) and finally, Particle Tracking Velocimetry (White and Shulz, 1977, Rice et al., 1995, Rice et al., 1996, Beladjine et al., 2007, Wang et al., 2008, Gordon and McKenna Neuman, 2009, Zhang et al., 2014, O'Brien and McKenna Neuman, 2016). Such instruments can provide a high resolution (i.e. sub-millimeter) description of the variation in saltation intensity along a vertical profile, and in the case of PTV, can track an individual particle throughout much of its lifecycle in saltation. However, considerable challenges remain with sampling large concentrations of particles within a saltation cloud that has reached saturation, and in particular, with accurate measurement of each particle diameter as required for assessment of the dynamics of the near bed transport phenomenon. This in turn limits the capability of geomorphologists to validate both large scale wind erosion models that require a thorough understanding of transport processes, as well as models of the development of small scale aeolian bedforms and their stratigraphy, as for example, impact ripples.
This paper builds upon recent PTV work by O'Brien and McKenna Neuman (2016) in which automated image processing that employs Expected Particle Area Searching (EPAS-PTV) was used to identify particle trajectories captured via high speed photography in the Trent Environmental Wind Tunnel (TEWT). The particle concentration was observed to decrease and the trajectory angle increase as the orientation of the vertical light sheet, in which the sampled particles were illuminated, increased in 5° increments from 0° (wind aligned) through to 60°. The results suggest that a large proportion of low velocity particles move at high spanwise angles relative to the mean airflow, likely as reptators. The vertical profile of the particle concentration was not considered at the time. The central objective of the present work aims to extend the analysis of the 1.5 Terabyte data set to obtain a high resolution, near-bed vertical profile of the particle dynamics captured in the original wind tunnel experiment over a range of spanwise angles. As described in the section to follow, the primary methodological advancement associated with the present paper concerns a calibration of the particle image size in pixels to determine the equivalent physical diameter (∼ length of the intermediate axis, also known as width) of the saltating particle, as would be determined through conventional sieve analysis.
Section snippets
Wind tunnel facility and general experimental design
The data set required for the present analyses was captured during 39 particle tracking experiments carried out in the environmental wind tunnel at Trent University in 2015. A short synopsis of these experiments is outlined below, while further details can be found in O'Brien and McKenna Neuman (2016).
The TEWT is a low speed, boundary-layer wind tunnel with an open-loop, suction-type design (see http://people.trentu.ca/~cmckneuman/website/facilities.html). It is housed within a large
Vertical variation of the particle transport rate and streamwise particle velocity
To determine the vertical distribution of the particle transport rate, used herein to approximate the mass flux, paired particle images were assigned to segmented bins at intervals of 500 μm with the bed surface defined as the zero plane of reference, as described in section 2.2 and illustrated in Fig. 3a. The normalized particle transport rate, expressed as a frequency for each segmented bin, was then calculated as,where nj,θ is the number of particle image pairs identified in the j
Discussion
Reports on the vertical profile of the horizontal particle flux vary greatly, depending on the setting in which measurements were taken, as well as the measurement approach. Saltation sampled in wind tunnels tends to produce flux profiles that are compressed vertically, with particles travelling in shorter hops and forming ripples of smaller wavelength as compared with field observations. While differences in turbulence scaling between field and lab settings offer a possible explanation for
Conclusions
Prior to the present study, measurements of the vertical profile of the particle transport rate and saltation dynamics have been conducted in a 2-dimensional context, and have lacked the precision needed to calculate the kinetic energy of individual saltating particles. By sampling at elevations as low as 50 μm from the bed surface, and at sufficient resolution to segment the vertical profile of particle mass and 3D-component velocity in increments of 500 μm, this study provides a novel data set
Acknowledgements
Funding in support of this work was provided through grants to C. McKenna Neuman from the Natural Sciences and Engineering Research Council of Canada (Discovery Grant) and the Canadian Foundation for Innovation (Microenvironments Laboratories). Early discussions with Dr. Jasper Kok and Hezi Yizhaq provided the incentive to pursue much of the work described in this paper, and in particular, inspired our attempt to measure the spanwise components of saltation. The authors also wish to acknowledge
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