On the boundary conditions for Lagrangian plastic transport models

Abstract: Lagrangian transport models (LTMs) have been widely used in the study of riverine and marine plastic pollution. However, the implementation of boundary conditions for LTMs is not well established when compared to conventional Eulerian modelling. Our paper aims to investigate boundary conditions for turbulent particle transport in open-channel flows at the free-surface, which is anticipated to facilitate future numerical transport studies. In our research, we implement different boundary conditions for the free-surface, including reflecting and absorbing boundaries, and we demonstrate their effects on the resulting concentration profile. The tested boundary conditions treat advection and diffusion steps separately, and we assume a probability for particles to detach from the interface, which serves as a preliminary step prior to establishing more physical detachment conditions. As such, our results demonstrate the impact of surface detachment on the concentration profile, which is compared to an analytical solution for plastic concentration, i.e., the modified Rouse profiles for rising particles. Overall, our research constitutes a first step towards a unifying framework for LTM boundary conditions, aiming to ensure better comparability of future simulation results. Keywords: Lagrangian particle transport, boundary conditions, riverine plastic pollution