Cellular model for sand dunes with saltation, avalanche and strong erosion: collisional simulation of barchans

Abstract

Barchans are crescent-shaped dunes that form under unidirectional wind in areas of limited sand supply. The recent development of flume experiments and computer simulations has renewed interest in the interaction dynamics of two or more barchans. From the flume experiment, four distinguishable types of collision patterns between two barchans have been observed: coalescence, ejection, split and reorganization. We have proposed a simple cellular model for numerical simulations of dune dynamics, in which saltation and avalanche are elementary processes. In the present paper, we first describe the model in detail. The model reproduces three types of collision patterns: coalescence, ejection, and reorganization. The largest reason for a split pattern not to occur is the lack of an effect of the flow separation at the brink line of dunes and the recirculation bubble that it produces. We then model the effect of the recirculation bubble by assuming that strong erosion occurs at the reattachment point of the separation flow. The strong-erosion model successfully reproduces all the collision patterns. Thus, three elementary processes -saltation, avalanche and strong-erosion -are sufficient for a phenomenological description of the interaction dynamics of aqueous barchans. It is also shown that the type of collision is determined by competition between the filling-up of the interdune between two barchans and the change in height of each dune.

Real barchan dune collisions and ejections

“…The mechanism we propose to account for this outcome involves mass transfer through sheltering and absorption of sediment by the upwind dune coupled with turbulent, unsaturated airflow that erodes a gap between the dunes. Our observations and interpretations confirm the main sequences of the collision‐ejection process noted in flume experiments, simulations and satellite imagery [ Endo et al , 2004; Katsuki et al , 2011; Vermeesch , 2011], and highlight the role of dune‐dune interactions in regulating the dune‐size distribution of barchan dune fields.…”

“…Despite considerable progress in resolving the morphology and kinematics of barchans, our understanding of their dynamics and interactions is still limited by the long timescales required to resolve changes. To this end, flume experiments and numerical models have been used to supplement field observations [e.g., Schwämmle and Herrmann , 2003; Endo et al , 2004; Hersen et al , 2004; Durán et al , 2005; 2011; Hersen , 2005; Hersen and Douady , 2005; Katsuki et al , 2011]. These approaches are invaluable for providing insight and developing hypotheses; however, there are few real‐world examples that have been used to verify and refine model and laboratory simulations.…”

“…When the dune‐size ratio is large, collisions typically result in the smaller, upwind (‘impacting’) barchan being absorbed by the larger, downwind (‘impacted’) barchan. As the ratio decreases the number of possible outcomes increases, ranging from the creation of one of more barchan dunes along the arms of the downwind dune, to ejections of dunes from the slipface [ Schwämmle and Herrmann , 2003; Endo et al , 2004; Durán et al , 2005; Hersen , 2005; Hersen and Douady , 2005; Kocurek et al , 2010; Katsuki et al , 2011]. A similar range of outcomes is produced by changing the dune alignment.…”

Avalanche grainflow on a simulated aeolian dune

“…For instance, Andreotti et al [] model the evolution of a sand pile into barchan dunes by forcing the slipface to maintain an angle of 30°. Katsuki et al [] identify cells within their CAM model whose elevation exceeded that of the θ R and iteratively redistributed half of the excess sediment into adjacent cells until the slope is reduced to less than θ R . Similarly, the more detailed models of avalanche processes on dunes by Allen [] and Hunter [] attempt to provide realistic simulation of grainfall and the resulting lee slope development leading to avalanche initiation by modeling grainflow through a conservation of sediment principle and relaxation to θ R .…”

Remote sensing and spatial analysis of aeolian sand dunes: A review and outlook

“…The importance of dune form evolution has emerged as a top research priority in light of recent progress in numerical modeling and flume experiments (e.g., Schwämmle and Herrmann, 2003;Endo et al, 2004;Hersen et al, 2004;Durán et al, 2005;Hersen, 2005;Hersen and Douady, 2005;Durán et al, 2011;Katsuki et al, 2011). These approaches afford insight into dune dynamics and interactions and can be used to supplement the paucity of field observations.…”