Secondary flow and longitudinal sediment patterns in open channel flow over a bed of mobile particles

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Longitudinal ridges are flow-induced sediment patterns which form under turbulent conditions in open channels with a mobile bed of non-cohesive particles. These bed-forms, which are distinct from transverse ripples or dunes, entail important consequences for momentum and scalar transport, and they find a wide array of applications e.g. in hydraulics (river flow) and other technical particulate flow systems (chemical engineering). Their formation is closely linked to the existence of secondary flow in the plane perpendicular to the primary mean flow direction, which in turn can be related to spanwise inhomogeneities in the turbulent statistics. In order to investigate the intricate balance between the spanwise bed shear stress and gravity that leads to the development of sediment ridges, we propose to perform interface-resolved direct numerical simulation coupled with a discrete element method for the inter-particle contact. By considering both cases, with and without channel side walls, we will attempt to elucidate the influence of a priori existing secondary flow of Prandtl's second kind upon the process. The latter is believed to interfere constructively with the instability process underlying the formation of ridges, leading to a multi-cellular secondary flow pattern in the case with side walls and mobile sediment. The high-fidelity numerical experiments to be carried out in this project will allow us to extract information on the scaling properties of the longitudinal bed-forms and of the associated secondary motion. The data will be further utilized towards the goal of improving the state of the art in stability analysis of a flat bed with respect to spanwise perturbations. It can be expected that the present contribution will enhance our understanding of the particulate flow dynamics to such a degree that it will lead to improved engineering-type models of this problem in the future.