A two-species continuum model for aeolian sand transport

Abstract

Starting from the physics on the grain scale, we develop a simple continuum description of aeolian sand transport. Beyond popular mean-field models, but without sacrificing their computational efficiency, it accounts for both dominant grain populations, hopping (or 'saltating') and creeping (or 'reptating') grains. The predicted stationary sand transport rate is in excellent agreement with wind tunnel experiments simulating wind conditions ranging from the onset of saltation to storms. Our closed set of equations thus provides an analytically tractable, numerically precise and computationally efficient starting point for applications addressing a wealth of phenomena from dune formation to dust emission.A drawback of the two-species description has been that it is still conceptually and computationally quite demanding. For reasons of simplicity and computational efficiency, many theoretical studies have therefore chosen to reduce the mathematical description even further, to mean-field-type 'single-trajectory' models [6]. This may be justified for certain purposes, e.g. for the mathematical modelling of aeolian sand dunes, which are orders of magnitude larger than the characteristic length scales involved in the saltation process and thus not expected to be very sensitive to the details on the grain scale. Their formation and migration is thought to predominantly depend on large-scale features of the wind field and of the saltation flux, chiefly the symmetry breaking of the turbulent flow over the dune and the delayed reaction of the sand transport to the wind [7]. Moreover, the reptating grains, although they are many, are generally thought to contribute less to the overall sand transport, because they have short trajectories and quickly get trapped in the bed again. Therefore, it seems admissible to concentrate on the saltating particles. On this basis, numerically efficient models for one effective grain species that can largely be identified with the saltating grain fraction have been constructed. The Sauermann model [8] is a popular and widely used example of such mean-field continuum models. Onespecies models have become a very successful means of gaining analytical insight into [9][10][11][12][13][14] and to conduct efficient large-scale numerical simulations of [15][16][17][18][19] the complex structure formation processes caused by aeolian transport. The reduction to a single representative trajectory makes the one-species models analytically tractable and computationally efficient. However, it is also responsible for some weaknesses concerning both the way in which the two species are subsumed into one [5] and how they feed back onto the wind [12]. These entail imperfections in the model predictions, most noticeably a systematic overestimation of the stationary flux at high wind speed (see figure 5). Therefore, the one-species models have been criticized for their lack of numerical accuracy and internal consistency [5,20]. There is also a number of interesting phenomena that cannot be quantitatively mode...

Experimental and numerical study of Sharp’s shadow zone hypothesis on sand ripple wavelength

“…The most challenging one is the dependence of the wavelength on wind speed (Andreotti et al, 2013). Experimental (Rioual et al, 2000), numerical, and theoretical results Lämmel et al, 2012;Yizhaq et al, 2014) indicate that the mean reptation length does not depend on the wind shear velocity. Thus, the models based on Anderson's model (Anderson, 1987) that assume that the initial wavelength of the ripple is $6 times the mean reptation length, failed to explain the wavelength dependence on wind speed.…”

Analytical model for flux saturation in sediment transport

“…Although previous studies focused on this equilibrium flux (e.g. [12][13][14][15][16][17]), the dynamics of sediment landscapes is controlled by situations out-of-equilibrium. In particular, the sediment flux needs a spatial lag -the so-called saturation length, L s -to adapt to a change in flow conditions [18][19][20][21].…”

Midair Collisions Enhance Saltation

“…As opposed to experiments, the direct computer simulation of saltation, the main Aeolian transport process, offers the possibility of switching on or off the collisions between particles or of modifying the collision parameters, such as the coefficient of restitution. This allows, for the first time, to precisely determine the role of midair collisions during saltation.We discover that midair collisions are the key ingredient for understanding the relation between different concepts such as the splash [7,8], the soft-bed [9,10], and the distinction between saltons and reptons [11,12]. During saltation, particles are ejected from the granular bed in a splash, produced by the impact of fast particles, so-called saltons (yellow trajectory in Fig.…”