A Moment-Based Depth-Averaged K-ε Model for Predicting the True Turbulence Intensity over Bedforms

Abstract

Turbulence models are critical for depth-averaged flow models in at least two ways: (i) as closures for momentum equations and (ii) as indicators of the spatial variability in the turbulence intensity field, which is crucial for sediment transport and bedform evolutions. This paper introduces a novel moment-based depth-averaged k-ε turbulence (MDAKE) model that could be considered as a revised version for the standard k-ε Rastogi–Rodi (SDAKE) model and can be used to estimate the true values for the depth-averaged turbulence kinetic energy in more complex and varied flow conditions with accelerating–decelerating flow fields. The study in hand shows that the SDAKE model tends to overestimate the true depth-averaged turbulent kinetic energy (k¯u) by 50 to 130% in the benchmark case of uniform flow over a flatbed. Further, the SDAKE model assumes that the bed shear velocity is an appropriate scale for the generation terms of both turbulent kinetic energy and dissipation. When bed topographic features vary, a shear flow zone is formed and the assumption is invalid. Since most of the turbulence is generated by shear flow zones away from the bed, the SDAKE model’s estimates for the depth-averaged turbulent kinetic energy field are out of phase with measurements for the flow over a train of bedforms. Therefore, a newly developed depth-averaged KE model based on the moment concept (MDAKE) is presented here. The model replaces bed shear velocity with the integral moment velocity scale (u1). The calibrated MDAKE model is used to predict turbulent kinetic energy over a train of bedforms. The results of the MDAKE model are in phase and generally in reasonable agreement with the measurements.