  Data from direct numerical simulation of open channel flow over a
geometrically rough wall at a bulk Reynolds number of 2900, generated by
Chan-Braun et al. ["Force and torque acting on particles in a transitionally
rough open-channel flow", J. Fluid Mech. 684, 441--474 (2011),
10.1017/jfm.2011.311] are further analysed with respect to the time and length
scales of force and torque acting on the wall-mounted spheres. For the two
sizes of spheres in a square arrangement (11 and 49 wall units in diameter,
yielding hydraulically smooth and transitionally rough flow, respectively), the
spatial structure of drag, lift and spanwise torque is investigated. The
auto-correlation and spectra in time as well as the space-time correlation and
convection velocities are presented and discussed. It is found that the
statistics of spanwise particle torque are similar to those of shear stress at
a smooth wall. Particle drag and lift are shown to differ from spanwise
particle torque, exhibiting considerably smaller time and length scales; the
convection velocities of drag and lift are somewhat larger than those of
spanwise torque. Furthermore, correlations between the flow field and
particle-related quantities are presented. The spatial structure of the
correlation between streamwise velocity and drag/spanwise torque features
elongated shapes reminiscent of buffer-layer streaks. The correlation between
the pressure field and the particle drag exhibits two opposite-signed bulges on
the upstream and downstream sides of a particle.
