Antidune simulations using continuum-based models

Abstract

The interactions of supercritical flows with sand or gravel beds in river channels or tidal inlets lead to the formation of antidunes. These bedforms are generally identified as nearly periodic sedimentary patterns of symmetrical shape that are in phase with the surface waves in the flow and have important effects on flow resistance and bedload transport. In addition, they play a fundamental role on morphodynamical processes in estuarine systems, on the scour around hydraulic infrastructure, and their bed signature can help to interpret paleofloods from sedimentary records. Despite the importance and ubiquity of antidunes in environmental flows, very few numerical simulations have captured their dynamics. In this work, we develop a model that couples the shallow-water and Exner equations in two-dimensions (2D) and demonstrate that a higher-level theory can reproduce the experimental antidune results of Pascal et al. (2021), independent of interactions at the particle scale. The flows are characterised by Froude numbers between 1.31 and 1.45, sediment diameters of $d_{50}=2.9$ mm and with 3° mean bed slopes. Using this information, we aim to identify the minimum requirements for a numerical model to capture in detail the migration of these bedforms. We use spectral analysis and compute statistics of bed elevation to determine the relevant temporal and spatial scales associated to the antidune propagation. The results of the model yield new insights on the mechanisms of bedform migration, providing tools to improve their description and assess the morphodynamic feedbacks.