Modeling Tracer Stone Dispersal with Continuously Supplied Tracers

Previous research with tracer stones has been conducted to study particle entrainment and displacement in the field and in the laboratory. In these experiments, tracers were placed in the bed deposit and their streamwise dispersal was monitored. Here we present a study of tracer dispersal from a continuously supplied source rather than an installment in the bed, using an analytical model. This approach can provide a better understanding on tracer dispersal over different periods of time from, for example, a contaminated source. Our numerical runs simulated experiments that could be conducted in a lab, using 1 mm uniform sand in a 7 m long, 0.2 m wide glass flume. Flow conditions were selected to create dunes with different combinations of flow and sediment feed rates. Flow rates ranged from 10 l/s to 20 l/s and sediment feed rates ranged from 240 g/min to 600 g/min. Model results show how the volume fraction content of tracers in the deposit varied in 4 vertical layers, in the streamwise direction and in time. Numerical runs were performed to reach equilibrium, that is when the volume fraction content of tracers at respective streamwise coordinates remained unchanged over time. The comparison of numerical runs with the same feed rate and different flow rates shows that equilibrium is reached most rapidly in the runs with the lowest flow rate. This happens because the volume fraction content of tracers in the non-equilibrium deposit is highest in the runs with low flow rates. Equilibrium was also reached more quickly in cases with the highest feed rate when flow rates remained unchanged. Results from the analysis of the various flow conditions suggest that equilibrium is reached first in the topmost layer and later in the layers below it. In addition to this, in the presence of high dune heights, particles become buried deeper in the deposit than in runs with small dunes therefore making the high dune cases take longer to reach equilibrium.