Sediment diffusion in deterministic non-equilibrium bed load transport simulations

The objective of this paper is to examine the importance of sediment diffusion relative to advection in bed load transport. At moderate bottom shear stress, water turbulence is too weak for picking up and keeping particles in suspension and so shallow water flows over erodible slopes carry sediment as bed load. Two deterministic frameworks are routinely used for studying bed load transport in sedimentation engineering and computational river dynamics. In equilibrium theory, the sediment transport rate is directly related to the water discharge (or bottom shear stress) independently of the intensity of sediment transport and the flow conditions (nearly steady flow as well as non-uniform time-dependent flow); embodied in the Exner equation, the bedload transport equation dictates bed evolution. In non-equilibrium (or non-capacity sediment transport) theory, sediment transport results from the imbalance between particle entrainment and deposition. Generally, sediment diffusion is included in none of these approaches. Based on recent advances in the probabilistic theory of sediment transport, this paper emphasizes the part played by particle diffusion in bed load transport. In light of these new developments, we revisit the concepts of adaptation length and entrainment rate, two essential elements in the deterministic non-equilibrium bed load theory. Using the shallow water equations, we ran numerical simulations of channel degradation and anti-dune development in gravel bed streams over steep slopes, which showed that sediment diffusion is as significant as advection in flume experiments. The predictive capability of deterministic models can thus be improved by including diffusion in the governing equations. We also present a versatile numerical framework, which makes it possible to use either deterministic or stochastic formulations of bed load transport.