Intermittent Grain Activity From Grain‐Scale Collective Entrainment Rules

Abstract In bed load sediment transport, grains are moved by turbulent flow and are in nearly continuous contact with other grains, resulting in sediment flux that is intermittent, displaying bursts of activity in both space and time. Understanding the dynamical origin of these fluctuations is a challenge. Grain‐scale models resolve the grain‐fluid coupling and provide insight into the grain‐scale sources of fluctuations, but are impractical to apply at the channel scale. On the other hand, landscape evolution models and other continuum treatments of alluvial channels ignore fluctuations by averaging over grain‐scale processes. We introduce an intermediate‐complexity lattice model, or cellular automaton, of bed load sediment transport with grain dynamics based on a simple set of rules. Mimicking collision interactions, grains in our model are entrained by their mobile neighbors with a probability that depends on the local bed slope. When a grain is entrained from or deposited onto the bed, it changes the bed elevation, providing a feedback between entrainment and bed topography. Despite this simplified representation of grain dynamics, the model reproduces the intermittent statistics of grain activity observed in previous studies. Numerical experiments further reveal how intermittency depends on bed width and point to a physical explanation. Finally, we use our model to derive a stochastic partial differential equation describing the system, providing a direct connection between collective entrainment and a nonlinear source term for grain entrainment, which is responsible for the intermittent dynamics.