Date of Award

Summer 2023

Document Type

Open Access Thesis


Civil and Environmental Engineering

First Advisor

Enrica Viparelli


Individual movement of sediment grains is oftentimes studied with the use of tracer stones. Studies performed both in the field, in the laboratory and with numerical models involve installing a patch of stones (tracers) on the bed surface and rarely deep in the deposit. Once installed, particle displacement is monitored over time scales varying from one flood to several years. These studies are useful, for example, to study bedload transport dynamics, understand contaminant fate and transport as well as to identify and define stream restoration practices (e.g. quality of fish habitat). Here we use a vertically continuous model to study tracer dispersal when tracers are supplied from upstream at a constant rate. In particular, particle dispersal is examined in both the streamwise and vertical directions. The mathematical formulation is simplified by assuming uniform particle size where particle deposition is modeled in terms of a constant step length in an equilibrium bed. Numerical runs were made to simulate laboratory experiments and investigate the effects of sediment size, sediment transport rate, and bed level irregularities on the evolution toward an equilibrium tracer concentration profile in the alluvial bed. Simulations were performed until an equilibrium condition was reached, meaning the volume of tracers in the streamwise and vertical directions did not significantly change in time. At equilibrium, the volume of tracers present throughout the deposit was smaller in cases with large sediment sizes than in cases with small sediment sizes. In addition, smaller particles were shown to be present deeper in the deposit than coarser sediment sizes. In cases of high sediment transport rate, the average tracer elevation at equilibrium was lower than in runs with small sediment transport rate, indicating that particles were buried deeper in the deposit. In runs with large bed level irregularities, particles were buried deeper in the deposit than in cases having small irregularities. In addition to this, as more vertical mixing occurred with higher dune heights, these cases took longer to reach an equilibrium state. The observed equilibrium tracer concentrations were the results of the interaction between the magnitude of bed level change around the mean value and the elevation of the maximum probability of particle entrainment in transport.


© 2023, Amanda Grace Balkus