Open-channel flow over evolving subaqueous ripples

We have numerically investigated the turbulent flow and sediment grain motion in an open-channel flow configuration over a subaqueous sediment bed featuring two-dimensional transverse ripples at moderate Reynolds number and super-critical Shields number values. The simulation data, which were generated by means of particle-resolved direct numerical simulation, are the same as in our previous work (Kidanemariam & Uhlmann, J. Fluid Mech., vol. 818, 2017, pp. 716-743). By carefully choosing the computational box sizes, we were able to accommodate single ripple units which form over an initially flat sediment bed at a wavelength equal to the domain length. The ripples then evolve into their asymmetric shape relatively quickly and eventually migrate downstream steadily while maintaining their shape and size. In the present study, using a ripple-conditioned phase-averaging procedure, we are able to obtain novel insights into the evolution of the turbulent flow and particle motion over the bedforms, in particular the spatial structure of the basal shear stress and its relation to the particle flow rate. Our analysis confirms that the boundary shear-stress maximum is located upstream of the ripple crest, while the particle flow rate is essentially in phase with the ripple topology, with an average phase difference between the two in the range of 18-19 particle diameters for the considered parameter values. We were further able to confirm the link between the sediment flux relaxation behaviour and the observed shear-stress/geometry lag, by direct evaluation of the saturation length scale.