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

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.

Modeling the Cross‐Sectional Dynamics of Tidal Sandbanks in Sediment‐Scarce Conditions

“…Therefore, the crest‐to‐crest distance cannot increase in our simulations, as has been observed for tidal and fluvial dunes (Nnafie et al., 2020; Porcile et al., 2020). Second, our model cannot simulate along‐bank variations in topography, whereas tidal and fluvial dunes develop more irregular and isolated crestlines, including barchans, when sediment is scarce (Endo, 2016; Kleinhans et al., 2002; Nnafie et al., 2020). Findings from tidal and fluvial dunes cannot be applied to tidal sandbanks due to their distinct flow‐topography interactions, but may inspire further research into bank shapes under scarcity.…”

“…Dynamic equilibria for bank shapes that varied in both horizontal dimensions were obtained by with bank ends periodically oscillating in time. Besides equilibrium conditions, long-term 2023) for tidal dunes and on Kleinhans et al (2002), Tuijnder et al (2009), Dreano et al (2010), Endo (2016), andVah et al (2020) for fluvial dunes.…”

“…Huthnance (1982a, 1982b) implemented scarcity as a non‐erodible layer and hypothesized that scarcity was required for equilibrium cross‐sections to exist, but later studies with more realistic hydrodynamics (e.g., Roos et al., 2004; Yuan et al., 2017) showed that this was not the case. Regarding other bedforms, sand scarcity was shown to decrease height and width, increase wavelength and three‐dimensionality in shape, and affect the migration rate of tidal (Nnafie et al., 2023; Porcile et al., 2017) and fluvial dunes (Dreano et al., 2010; Endo, 2016; Kleinhans et al., 2002; Tuijnder et al., 2009; Vah et al., 2020). However, these bedforms are driven by flow circulations in the vertical plane (Hulscher, 1996; Paarlberg et al., 2009; Vittori & Blondeaux, 2020) rather than the residual circulations in the horizontal plan that drive tidal sandbanks (Figure 1).…”