[1] We present a new 3-D cellular automaton model for bed form dynamics in which individual physical processes such as erosion, deposition, and transport are implemented by nearest neighbor interactions and a time-dependent stochastic process. Simultaneously, a lattice gas cellular automaton model is used to compute the flow and quantify the bed shear stress on the topography. Local erosion rates are assumed to be proportional to the shear stress in such a way that there is a complete feedback mechanism between flow and bed form dynamics. In the numerical simulations of dune fields, we observe the formation and the evolution of superimposed bed forms on barchan and transverse dunes. Using the same model under different initial conditions, we perform the linear stability analysis of a flat sand bed disturbed by a small sinusoidal perturbation. Comparing the most unstable wavelength in the model with the characteristic size of secondary bed forms in nature, we determine the length and time scales of our cellular automaton model. Thus, we establish a link between discrete and continuous approaches and open new perspectives for modeling and quantification of complex patterns in dune fields.

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[1] We analyze the morphodynamics of bedforms produced under unidirectional flow conditions by a lattice gas cellular automaton designed to study sediment transport. In this model, the same instability is responsible for the formation of dunes on flat sand beds and the initiation of superimposed bedforms on dune slopes. In transverse dune fields, secondary bedforms increase crestline sinuosity and number of defects (end of crestlines). On the other hand, avalanches and lateral grain motions tend to eliminate these defects to produce more regular crestlines. Lateral fluxes of sediment are also essential for stabilizing the shape of isolated barchan dunes. We measure the propagation speed of superimposed bedforms on steady state barchan dunes and show how they contribute to the formation and detachment of smaller barchans along horns. The model predicts that barchan dunes are not scale invariant and that their shape varies with respect to the strength of the flow. In addition, we show that the increase in bed shear stress between the ground and the crest is proportional to the dune aspect ratio. Finally, we present a general methodology for estimating the sediment flux over the brink from dune aspect ratio and flow velocity. Using these fluxes, we rescale the propagation speed of different generations of bedforms to verify that dunes and secondary bedforms are dynamically identical. Despite more fluctuations than in the case of isolated barchan dunes, all these geometric and dynamical relationships hold for a population of dunes with complex dune-dune interactions.