Modelling dune evolution and dynamic roughness in rivers

Abstract

Accurate river flow models are essential tools for water managers, but these hydraulic simulation models often lack a proper description of dynamic roughness due to hysteresis effects in dune evolution. To incorporate the effects of dune evolution directly into the resistance coefficients of hydraulic simulation models, we developed a dynamic roughness model consisting of: (1) a process-based simulation model to predict dune dimensions, and (2) an empirical roughness predictor to translate computed dune dimensions into a resistance coefficient. The dune evolution model solves the shallow water equations in a vertical plane using hydrostatic pressure conditions. The sediment transport is modelled using a Meyer-Peter Muller type of formulation including gravitational bed-slope effects. The separation streamline, the upper boundary of the flow separation zone, forms an artificial bed in the region of flow separation. Sediment transport in the flow separation zone is assumed to be zero and sediment passing the flow separation point deposits on the leeside of the dune. Computed dune dimensions, migration rates and times to equilibrium compare reasonably well with various flume data sets. Flow separation is shown to be crucial to take into account for modelling dune evolution: if flow separation is not included, dune shapes are incorrectly predicted and the dune height saturates at an early stage of bedform evolution, yielding an underprediction of dune height and time to equilibrium. The local bed slope at the dune crest also plays a crucial role to obtain saturation at an equilibrium dune height. The dynamic roughness model is coupled with the 1-dimensional hydraulic simulation model Sobek. The resulting model can be applied to simulate water levels in natural river settings at river reach spatial scales and flood wave time scales, explicitly taking the time-evolution of river dunes into account. The hysteresis of dune dimensions and roughness coefficients is larger for broad-peaked flood waves than for sharp-peaked flood waves, since the relatively long period of high river discharge gives the dunes ample time to increase in height. This emphasizes the importance of the flood wave shape for dune evolution and thus roughness predictions.