  Direct numerical simulation of open-channel flow over a bed of spheres
arranged in a regular pattern has been carried out at bulk Reynolds number and
roughness Reynolds number (based on sphere diameter) of approximately 6900 and
120, respectively, for which the flow regime is fully-rough. The open-channel
height was approximately 5.5 times the diameter of the spheres. Extending the
results obtained by Chan-Braun et al. (J. Fluid Mech., vol. 684, 2011, 441) for
an open-channel flow in the transitionally-rough regime, the present purpose is
to show how the flow structure changes as the fully-rough regime is attained
and, for the first time, to enable a direct comparison with experimental
observations. The results indicate that, in the vicinity of the roughness
elements, the average flow field is affected both by Reynolds number effects
and by the geometrical features of the roughness, while at larger
wall-distances this is not the case, and roughness concepts can be applied. The
flow-roughness interaction occurs mostly in the region above the virtual origin
of the velocity profile, and the effect of form-induced velocity fluctuations
is maximum at the level of sphere crests. The spanwise length scale of
turbulent velocity fluctuations in the vicinity of the sphere crests shows the
same dependence on the distance from the wall as that observed over a smooth
wall, and both vary with Reynolds number in a similar fashion. Moreover, the
hydrodynamic force and torque experienced by the roughness elements are
investigated. Finally, the possibility either to adopt an analogy between the
hydrodynamic forces associated with the interaction of turbulent structures
with a flat smooth wall or with the surface of the spheres is also discussed,
distinguishing the skin-friction from the form-drag contributions both in the
transitionally-rough and in the fully-rough regimes.
