Approximate methodology to account for effects of coherent structures on sediment entrainment in RANS simulations with a movable bed and applications to pier scour

Movable-bed Reynolds-Averaged Navier-Stokes (RANS) simulations of local scour around bridge piers and abutments without ad hoc corrections tend to underestimate scour. This is generally attributed to the inability of RANS to accurately capture the unsteady dynamics of the large-scale coherent structures forming in the bed vicinity. Moreover, the characteristics of these coherent structures and their erosive capacity are expected to change as the bed evolves toward equilibrium. In the present study, Detached Eddy Simulations (DES) of flow past circular and rectangular piers are performed with bathymetry corresponding to different stages of the scour process between initial (flat-bed) conditions and equilibrium scour conditions to better understand how the coherent structures drive scour around the pier at different stages of the scouring process and to assess the capabilities of RANS to predict the flow and the turbulence statistics. Using these results, a new methodology is proposed to account for the effects of large-scale coherent structures on sediment entrainment that is directly applicable to RANS simulations with movable bed. The main idea is to improve the predictions of the local flux of sediment entrained from the bed by considering the effect of bed friction velocity fluctuations induced by the coherent structures situated near the bed, a critical effect that is generally neglected in RANS simulations. The new methodology is based on augmenting the bed friction velocity available from the time-accurate RANS calculation by a term that is proportional to the standard deviation of the bed friction velocity. This term is estimated from the turbulent kinetic energy field predicted by RANS. The model has one free parameter. Its value is calculated such that for fixed bed simulations the total entrainment flux predicted by the time-accurate RANS matches the value predicted by DES. Based on simulations conducted for flow past circular and rectangular piers, the value of the free parameter was estimated to be between 1.5 and 4, with lower values recommended to be used for cases when the time-accurate RANS simulation captures the large-scale vortex shedding behind the pier. Movable bed simulations performed using the augmented bed friction velocity model are shown to predict much more accurately the maximum scour depth around circular and rectangular piers compared to the corresponding simulations where the entrainment flux was calculated only based on the local value of the bed friction velocity calculated from the RANS velocity field