Sediment transport on rippled beds

We conduct an Euler-Lagrange, direct numerical simulation of a turbulent channel flow at a shear Reynolds number of Reτ=180 over an erodible particle bed. The particle bed consists of approximately 1.3 × 106 monodisperse particles, resulting in a bed thickness of around 12–13 particles. The particle density and size are chosen to achieve a ratio of 4 for the Shields stress to the critical Shields stress necessary for incipient motion such that particle transport occurs primarily as bedload. The simulation is run long enough for ripples to form. We track the temporal evolution of the particle flux and excess Shields stress for the entire bed as well as for the four regions of a ripple, namely, the crest, trough, lee side, and stoss side. We find that the particle flux and excess Shields stress closely match the Wong and Parker correlation when the particle bed is featureless at early time but diverge from the correlation when ripples form. This deviation primarily arises from particle transport in the trough and lee side regions. Conversely, particle transport in the crest and stoss side regions remains largely consistent with the Wong and Parker correlation. A root mean square-based correction for the bed is proposed to be used in conjunction with the Wong and Parker correlation. Additionally, ripples attain a self-similar profile in the shape and near-bed shear stress when they are sufficiently distant from their upstream neighbor. Any departure from self-similarity occurs when the upstream neighbor gets within close proximity.