Direct Numerical Simulation of Turbulent Boundary Layer Flows Over a Permeable Bed Using Continuum and Pore-Resolved Approaches*

A direct numerical simulation (DNS) is performed for a turbulent boundary layer over a porous sediment bed at permeability Reynolds number of Re_K= 2.56 (Re_τ=270) representative of aquatic systems. A continuum approach based on the volume-averaged Navier-Stokes (VANS) equations is used by defining smoothly varying porosity across the bed interface and modeling the drag force in the porous bed using a modified Ergun equation with Forchheimer corrections for inertial terms (Wood et al., Annual Review of Fluid Mechanics, 2020). The results from the continuum approach DNS are compared with a pore-resolved DNS in which turbulent flow over a randomly packed sediment bed is performed using a fictitious domain method to enforce the rigidity and no-slip condition on the monodispersed spherical particles representing the sediment bed. A spatially varying porosity profile generated from the pore-resolved DNS is used in the continuum approach. Mean flow and Reynolds stress statistics and net momentum exchange between the free-stream and the porous bed are compared between the two DNS studies, showing good agreement. The continuum VANS approach allows for a significant reduction in the computational costs thereby allowing to study hyporheic exchange of mass and momentum in large scale aquatic domains with combined influence of bedform and bed roughness.