Subaqueous ripples and dunes dominate the hydraulic roughness and sediment exchange of sandy alluvial rivers, yet reach-scale morphodynamic models still predict their effect with empirical equilibrium bedform-dimension formulas plus ad hoc time-lag corrections. Nabi et al. (2013) showed that detailed three-dimensional, physics-based simulation of turbulent flow and sediment transport can reproduce ripple and dune generation and migration in the laboratory, and pointed to the follow-on potential of such simulations: constituting a basis for bed-roughness and sediment-transport parameterization under steady as well as varying flow conditions for use in large-scale morphodynamic models, extendable to the rare extreme discharges on which flood-protection design standards rest. The open problem is this downscaling closure: capture the process-scale bedform dynamics that detailed simulations reveal — generation, migration, splitting, merging, and superimposition of bedforms — in a parameterization that reach-scale models can afford, valid under steady and varying flow including the hysteretic response of bedforms to flood waves observed in flume and field studies, and validate it against laboratory and field data across flow regimes. Later work (2014–2026) has parameterized individual mechanisms and documented how poorly understood pieces remain, but no validated general closure exists.

Background

Ripples and dunes are wavelike bed elevations that form on sandy river beds by the interaction of the flow with sediment motion: ripples are small-scale (centimetres) bedforms, dunes are larger (heights typically 10–30% of the water depth) with gentle upstream (stoss) slopes and steep downstream (lee) slopes where the flow separates. Because the flow does work on these forms, they act as hydraulic roughness — a resistance to the flow that raises water levels — over and above the skin friction on the grains themselves; this extra resistance is called form drag or form roughness. Predicting stage, navigable depth, and bed evolution in sandy rivers therefore requires predicting bedform dimensions and their roughness contribution.

Classical engineering practice uses equilibrium predictors: empirical formulas giving dune height and length as functions of flow depth, velocity, and grain size, with a roughness height derived from them. Under flood waves, dunes adapt with a time lag, and simple time-lag corrections are applied to the equilibrium values. These closures carry little of the underlying physics. In particular, bedforms evolve through discrete interactions — new bedforms are created on long stoss sides, split, merge with neighbours, and migrate at speeds that depend on their height, so smaller superimposed bedforms overtake and amalgamate with larger ones — and these interactions, not smooth growth, control the statistics of bedform size. Reviewing the field, Best (2005) identified bedform dynamics and its roughness implications as a central open direction.

Nabi, de Vriend, Mosselman, Sloff, and Shimizu (2013) advanced the process side: they simulated ripples and dunes with a three-dimensional model in which turbulence is resolved by large eddy simulation (LES — a technique that computes the large turbulent eddies directly and models only the smallest scales), sediment is tracked as individual particles through pickup, motion near the bed, suspension, and deposition, and the bed evolves by a sediment balance of these sources and sinks. The model reproduced five laboratory dune experiments, the effect of grain size on ripple superimposition, and local scour around a pier (validated against the experiments of Khosronejad et al. 2012). The authors state four limitations framing the open problem: (i) the generation, migration, splitting, merging, and superimposition of dunes under constant or variable discharge were then studied by only a few attempts and were "still not fully understood"; (ii) full verification of three-dimensional model performance was hampered by a lack of measured three-dimensional ripple and dune data; (iii) the LES wall function (the near-bed turbulence treatment) overpredicted bed shear stress where the geometry forces recirculation or rapid acceleration, causing too-fast computed scour in the first minutes at the pier; and (iv) their model "has the potential to constitute a basis for bed roughness and sediment transport parameterization under steady as well as varying flow conditions for use in large-scale morphodynamic models", with extension to rare extreme events needed when flood-protection design is based on return periods of centuries or millennia. Detailed simulations of this kind are far too expensive to run inside a reach-scale model, which is exactly why a parameterization derived from them is required.

Problem Statement

Derive, from the physics captured by detailed three-dimensional process-based simulations of subaqueous ripples and dunes — turbulent flow resolved by large eddy simulation coupled to particle-based sediment transport, as in Nabi et al. (2013) — and from the bedform dynamics such simulations and experiments reveal (generation, migration, splitting, merging, and superimposition of bedforms), a parameterization of bed-form-induced hydraulic roughness and of the associated sediment exchange that can be used in large-scale (reach-scale) morphodynamic and flood-propagation models. The parameterization must be demonstrated under steady as well as varying flow conditions, and must state a physically justified basis for extrapolation to the rare extreme discharges on which flood-protection design with return periods of centuries or millennia depends. It must be validated against independent laboratory and field data — bedform dimensions, migration, and roughness or water-level effects. The single objective uniting all requested results is to replace equilibrium bedform-dimension predictors with ad hoc time-lag corrections by a closure that carries process-scale bedform dynamics into reach-scale prediction of water level and bed evolution.

References

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