The development of stochastic based transport models to predict the advection and diffusion of bed-load sediment

Many morphological and environmental problems in rivers are associated with the transport of sediment, in particular with the movement of material along the stream bed. The complex nature of turbulent flow and the variability inherent within granular beds, along with the mutual influence one plays on the other, can only be described using the concepts of probability. It follows that the intermittent motion of bed-load particles can be termed by random variables. The stochasticity of key variables has been recently identified as a source of diffusion, i.e. suggesting that a plume of bed-load grains tends to spread while moving in the main flow direction. In this study the application of a Lagrangian analysis to existing high-frequency measurements of moving natural gravel particles contained in a tracking database helped to identify and scale the diffusive regimes related to different stages of grains' motion. Lagrangian tracking data allowed for an in-depth, study of the stochasticity of the particle step length, i.e. the single longitudinal distance computed by a grain from the entrainment to the deposition. The information on the distributed step lengths is then incorporated into a modified version of the Exner mass balance equation which has been developed to model the experimental advective and diffusive transport observed in long duration flume experiments with graded bed deposits comprised of natural sand and crashed marble gravel that have been previously reported. The modelling results indicate that the relative size of bed roughness, together with the thickness of the mixing
surficial layer of the bed, play a major role in dictating the pattern of behaviour of particle motion. As the time-dependent burial depth of grains influences the vertical mixing and therefore the downstream diffusion of particles, concentrating the research only on the surficial motion of particles appears restrictive. In order to attain an insight view of the bed and to overcome the previous experimental limitations in terms of the description of the particle step distribution, a non-intrusive technique has been implemented in an annular
flume to track the time history of tracing grains subject to intermittent motion in a bed made of transparent glass beads. In the light of the new information on particle transport, a more general Exner-based model incorporates the idea that tracer particles arriving at position x at time t started their random hops r at many different times. Its application to the latest sediment tracer concentration data has proven to be promising in that convincing detailed descriptions of the observed advective and diffusive behaviour of bed-load transport were obtained.