Linear stability analysis of subaqueous bedforms using direct numerical simulations

We present results on the formation of ripples from linear stability analysis. The analysis is coupled with direct numerical simulations of turbulent open-channel flow over a fixed sinusoidal bed. The presence of the sediment bed is accounted for using the immersed boundary method. The simulations are used to extract the bed shear stress and consequently the sediment transport rate. The approach is different from traditional linear stability analysis in the sense that the phase lag between the bed topology and the sediment flux is obtained from the three-dimensional turbulent simulations. The stability analysis is performed on the Exner equation, whose input, the sediment flux, is provided from the simulations. We ran 11 simulations at a fixed shear Reynolds number of 180, but for different sediment bed wavelengths. The analysis allows us to sweep a large range of physical and modelling parameters to predict their effects on linear growth. The Froude number appears to be the critical controlling parameter in the early linear development of ripples, in contrast with the dominant role of particle Reynolds number during the equilibrium stage. We also present results from a wave packet analysis using a one-dimensional Gaussian ridge

Eroding Uncertainty: Towards Understanding Flows Interacting with Mobile Sediment Beds Using Grain-Resolving Simulations

Dense particle-laden flows play an important role in many environmental processes, including the shaping of rivers and the formation of landslides. Despite decades of study, researchers have not been able to accurately predict the onset of erosion and the amount of sediment transported by flows, due in part to the difficulty in measuring dense particle-laden flows. Highly-resolved numerical simulations, on the other hand, allow us to study the physics of particle-fluid and particle-particle interactions in much more detail.We develop a code to accurately simulate dense, polydisperse, particle-laden flows as well as methods by which to analyze them. The code solves the Navier-Stokes equations for the fluid phase and resolves the flow around each individual particle using an immersed boundary method. We also develop a collision model to accurately resolve particle-particle interactions within the fluid. We then perform simulations of a pressure-driven flow over a bed of spherical particles that agree with experimental results for particle velocities and flow rates. Using a control volume momentum balance, we analyze fluid and particle stresses within the simulations, which reveal the mechanisms by which the particle bed expands and contracts during changes in flow rates. These same stresses also allow us to measure the rheology of the particle-laden flows, where we find some agreement with existing constitutive models but also reveal the need to develop these models further