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A simple stochastic cellular automaton model is proposed for simulating bedload transport, especially for cases with a low transport rate and where available sediments are very sparse on substrates in a subaqueous system. Numerical simulations show that the bed type changes from sheet flow through sand patches to ripples as the amount of sand increases; this is consistent with observations in flume experiments and in the field. Without changes in external conditions, the sand flux calculated for a given amount of sand decreases over time as bedforms develop from a flat bed. This appears to be inconsistent with the general understanding that sand flux remains unchanged under the constant-fluid condition, but it is consistent with the previous experimental data. For areas of low sand abundance, the sand flux versus sand amount (flux–density relation) in the simulation shows a single peak with an abrupt decrease, followed by a long tail; this is very similar to the flux–density relation seen in automobile traffic flow. This pattern (the relation between segments of the curve and the corresponding bed states) suggests that sand sheets, sand patches, and sand ripples correspond respectively to the free-flow phase, congested phase, and jam phase of traffic flows. This implies that sand topographic features on starved beds are determined by the degree of interference between sand particles. Although the present study deals with simple cases only, this can provide a simplified but effective modeling of the more complicated sediment transport processes controlled by interference due to contact between grains, such as the pulsatory migration of grain-size bimodal mixtures with repetition of clustering and scattering.

Simple stochastic cellular automaton model for starved beds and implications about formation of sand topographic features in terms of sand flux