Results of sediment tracer studies in nearshore and beach environments indicate that mixing of sediment occurs within a sediment bed through thicknesses in excess of the maximum amplitude of the bed forms. This phenomenon may be important in problems related to coastal contamination by particulate pollutants. Hazardous concentrations may be established deep within a bed where mixing occurs very slowly. This may have the effect of storing pollutant within the bed for long time periods following an initial “spill”-type accident.
A tridiagonal Markov chain is adopted as a general model for describing mixing processes between adjacent layers within a bed and across the bed-fluid interface. For this model the statistical expectation of particle residence time within a bed depends only on the sediment exchange rate between the bed and the fluid, and the thickness of the bed through which mixing is possible. However, the variance of bed residence time also depends on the number of layers considered in the model and the manner in which transition probabilities vary among the layers. Several models are explored; for certain initial conditions, the predicted duration of contamination at a particular locality may exceed that predicted by the simple one-layer Einstein model by one or two orders of magnitude.