Abstract
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.
Highlights
Bedforms, including both subaerial and subaqueous ones, have been studied for more than half a century, mainly starting with the pioneering field observations of Bagnold (1941) and the laboratory studies of Allen (1968) and continuing to recent comprehensive experiments (e.g., Perillo et al 2014)
Development of sand topographic features First, to evaluate the present model, we qualitatively assessed the dependence of the topographic features on the amount of sand, as expressed by the average sand thickness, which is defined as the total number of sand slabs divided by the number of cells in the system
When the average sand thickness was less than 22, the ripples were barchans, an isolated type of ripple that typically takes a crescent shape (Fig. 2a); this is consistent with the Temporal changes in sand flux compared with flume experiments The sand flux is defined as the sand discharge per width
Summary
Bedforms, including both subaerial and subaqueous ones, have been studied for more than half a century, mainly starting with the pioneering field observations of Bagnold (1941) and the laboratory studies of Allen (1968) and continuing to recent comprehensive experiments (e.g., Perillo et al 2014). Previous CA models for aeolian dunes have attributed the bedform generation to changes in the saltation length, in the present study, which employs a stochastic model, we consider changes of the migration speed of sand particles that are in continuous contact with the bed (i.e., sand that moves no faster than one cell per time step).
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