  The effect of the Strouhal number on periodic forcing of the flow over a
backward-facing step (height, $H$) is investigated experimentally. Forcing is
applied by a synthetic jet at the edge of the step at Strouhal numbers ranging
from $0.21<St_H<1.98$ ($St_H = f H/U_\infty$) at a Reynolds number of $Re_H =
HU_\infty/\nu = 41000$. In the literature, the effect of Strouhal number on the
reattachment length is often divided into low- and high frequency actuation,
referring to different frequency modes in the unforced flow. In the present
paper, variations with Strouhal number are explained based on entrainment
rather than frequency modes. The reattachment length is shown to decrease
linearly with entrainment. Entrainment is driven by vortices generated by the
forcing and locally entrainment is shown to be qualitatively similar to
circulation for all cases considered. Total circulation (and therewith
entrainment and the effect on the reattachment length) is shown to decrease
with Strouhal number whereas this is not predicted by models based on frequency
modes. An empirical model for the (decay of) circulation is derived by tracking
vortices in phase-locked data. This model is used to decipher relevant scaling
parameters that explain the variations in circulation, entrainment and
reattachment length. A low-Strouhal-number regime is observed for which
vortices are formed at a late stage relative to the recirculation region,
causing a decrease in effectiveness. For high Strouhal numbers vortices are
being re-ingested into the actuator or are packed so close together that they
cancel each other, both decreasing the effectiveness of forcing. In the
intermediate regime a vortex train is formed of which the decay of circulation
increases for increasing Strouhal number. The scaling of this decay fully
explains the observed variation in reattachment length.
