The pattern of grainfall deposition in the lee of aeolian dunes

ABSTRACT
A simple model for the deposition pattern in the lee of aeolian dunes is presented that relies heavily upon a recently developed understanding of aeolian saltation. Grainfall deposition at any position on the lee face is the result of all saltation trajectories that leave any point on the surface of the dune upwind of the brink with sufficient initial velocity to travel the intervening distance. The deposition rate at any position on the lee slope is obtained by integrating over all combinations of initial position and required velocity, the velocity being weighted by its probability density.
The resulting calculated total deposition rate patterns show distinct maxima on the order of one to a few decimetres from the brink, beyond which deposition rates fall off roughly exponentially. An important length scale emerges that characterizes this decay with distance from the brink, the length increasing with wind velocity, and decreasing with grain diameter. It is shown that this length scale is on the order of one metre for typical grain size and wind conditions. That this is typically smaller than the length of the lee slope is what gives rise to the oversteepening and eventual avalanching of the lee sides of aeolian dunes. The position of a pivot point on the lee slope may be predicted, separating source regions from accumulation regions for grainflow avalanche deposits.
The calculated patterns provide not only a means for quantitative interpretation of active and fossil dune grainfall deposits, but they provide the initial geometry for grainflow avalanches. The initial failures should coincide with the steepest gradient in grainfall deposition, slightly downslope from the grainfall maximum.