  Pore-resolved direct numerical simulations (DNS) are performed to investigate
the interactions between streamflow turbulence and groundwater flow through a
randomly packed porous sediment bed for three permeability Reynolds numbers,
$Re_K$, of 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 (PDFs) of normalized local bed stress are
found to collapse for all Reynolds numbers and their root mean-squared
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 PDFs 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 can potentially be used in
providing better boundary conditions in modeling of incipient motion and
reach-scale transport in the hyporheic zone.
