Long-time evolution of models of aeolian sand dune fields: Influence of dune formation and collision

Theoretical models which approximate individual sand dunes as particles that move and interact via simple rules are currently the only viable method for examining whether large dune fields will evolve into a patterned structure. We find that these types of simulations are sensitive to the influx condition and interaction function, and are not necessarily robust under common assumptions. In this paper, we review continuum dune models and how they connect to models of dune fields that approximate dunes as interacting particles with collision and coalescence dynamics. This type of simple dune field model is examined under different boundary and initial conditions. We identify different long-term behaviors depending on model parameters as well as the way in which dunes are initialized and collide. A “rule” for predicting the end state of a modelled dune field is derived, based on the statistics of a uniform influx dune size distribution and the interaction function. Possible future adjustments to the multiscale model, such as the use of a Gaussian influx dune size distribution, and their effect on the prediction rule are also discussed.