River bedforms such as dunes, antidunes, steps and pools arise from flow instabilities, and their features are determined by both flow conditions and bed characteristics [1]. In most cases, dunes are observed under subcritical flow conditions, while antidunes appear under supercritical conditions [3]. The interaction between these bedforms and the flow field, especially in supercritical regimes, is not yet fully understood. Models based on the shallow-water equations include skin friction (i.e., turbulent dissipation caused by bed roughness), but usually ignore the extra stress created by the bedforms. For one-dimensional flows, the momentum balance equation of the shallow-water equations can be cast in non-conservative form (1):
h(∂u/∂t+u ∂u/∂x)+gh ∂h/∂t=-gh sinϴ-τ_b/ρ, (1)
where h is the water depth, u is the flow velocity, g is gravitational acceleration, 𝛳 is the bed inclination angle, τ_b represents the bed shear stress, and ρ is the water density. While the term 〖-τ〗_b /ρ accounts for bed roughness-induced friction, it does not explicitly capture the dynamic effects of bedform-induced stresses. In light of these complexities, the present study conducts experimental investigations to better understand how antidunes affect the flow field.
We conducted laboratory experiments in a flume of length 5.8 m and width 4 cm with a bed composed of well-sorted gravel of mean size 2.5 mm. To measure the flow field, we sieved polyamide particles (original d50 = 100 µm) using an 80 µm mesh to retain particles larger than 80 µm, which were then injected as tracers into the water flow. Accurate tracking of the tracers required the absence of bedload transport concurrently. Therefore, we forced the flow to reach a state referred to as stationary antidunes [2] before injecting tracers. We performed experiments with various slope and water discharge combinations while keeping other parameters constant. A high-resolution, high-speed camera was positioned along the side of the flume to capture a window encompassing a couple of antidunes. The video footage was analyzed using Particle Image Velocimetry (PIV) and Particle Tracking Velocimetry (PTV) techniques to calculate the flow field.
We compared turbulence parameters calculated from the velocimetry data against theoretical values suggested by the shallow-water equations. This comparison makes the case for a better evaluation of bed friction when bedforms significantly impact turbulence. Our preliminary results indicate that in the presence of antidunes, empirical values of turbulent kinetic energy are approximately 50% higher than the theoretical predictions. As a next step, we intend to propose an empirical parametrization of form drag for antidunes and supercritical flows and include it in a numerical model.
Our results demonstrate that antidunes significantly influence turbulence, highlighting the need for improved bed friction parameterizations in supercritical
