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A large eddy simulation (LES) is performed for a turbulent open channel flow over a porous sediment bed at permeability Reynolds number of ReK∼2.56 (Reτ = 270) representative of aquatic systems. A continuum approach based on the upscaled, volume-averaged Navier−Stokes (VaNS) equations is used by defining smoothly varying porosity across the sediment water interface (SWI) and modeling the drag force in the porous bed using a modified Ergun equation with Forchheimer corrections for inertial terms. The results from the continuum approach are compared with a pore-resolved direct numerical simulation (PR-DNS) in which turbulent flow over a randomly packed sediment bed of monodispersed particles is investigated [Karra et al.,J. Fluid Mech. 971, A23 (2023)] A spatially varying porosity profile generated from the pore-resolved DNS is used in the continuum approach. Mean flow, Reynolds stress statistics, and net momentum exchange between the freestream and the porous bed are compared between the two studies, showing reasonably good agreement. Small deviations within the transitional region between the sediment bed and the freestream as compared to the PR-DNS results are attributed to the local protrusions of particles in a randomly packed bed that are absent in the continuum approach but are present in the PR-DNS. A better representation of the effective permeability in the top transition layer that accounts for roughness effect of exposed particles is necessary. The continuum approach significantly reduces the computational cost, thereby making it suitable to study hyporheic exchange of mass and momentum in large scale aquatic domains with combined influence of bedform and bed roughness. 

Pore-resolved direct numerical simulations are performed to investigate the interactions between streamflow turbulence and groundwater flow through a randomly packed porous sediment bed for three permeability Reynolds numbers,$$Re_K=2.56$$, 5.17 and 8.94, representative of natural stream or river systems. Time–space averaging is used to quantify the Reynolds stress, form-induced stress, mean flow and shear penetration depths, and mixing length at the sediment–water interface (SWI). The mean flow and shear penetration depths increase with$$Re_K$$and are found to be nonlinear functions of non-dimensional permeability. The peaks and significant values of the Reynolds stresses, form-induced stresses, and pressure variations are shown to occur in the top layer of the bed, which is also confirmed by conducting simulations of just the top layer as roughness elements over an impermeable wall. The probability distribution functions (p.d.f.s) of normalized local bed stress are found to collapse for all Reynolds numbers, and their root-mean-square fluctuations are assumed to follow logarithmic correlations. The fluctuations in local bed stress and resultant drag and lift forces on sediment grains are mainly a result of the top layer; their p.d.f.s are symmetric with heavy tails, and can be well represented by a non-Gaussian model fit. The bed stress statistics and the pressure data at the SWI potentially can be used in providing better boundary conditions in modelling of incipient motion and reach-scale transport in the hyporheic zone.