Setting the length and time scales of a cellular automaton dune model from the analysis of superimposed bed forms

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.