A meso-scale gravel tracer model for gravel-bed rivers

This paper presents the mathematical and algorithmic derivation of a simplified numerical gravel tracer model that utilizes the flowfield calculated by a three-dimensional hydrodynamic model. It can simulate the pathways and velocities of multiple gravel tracers along several kilometers of river length. The model simplifies tracer shape as an equipotential ellipsoid, assumes constant tracer movement and incorporates the presence of rest periods into a transport resistance coefficient. It considers the influence of local bed slope and performs a random walk based on the near-bed turbulent kinetic energy. The deterministic shear stress value is permuted by a random variable that follows a Gaussian probability density function. The model was calibrated on data of 40 radio-acoustic tracer gravels monitored for more than a year at the Danube River. It was found that both paths and velocities of gravel tracers observed during the field experiment could be reproduced for different river discharges using the same transport resistance coefficient.