  Context. Velocity or intensity swirls have now been shown to be widely
present throughout the photosphere and chromosphere. It has been suggested that
these events could contribute to the heating of the upper solar atmosphere, via
exciting Alfv\'en pulses, which could carry significant amounts of energy.
However, the conjectured necessary physical conditions for their excitation,
that the magnetic field rotates co-spatially and co-temporally with the
velocity field, has not been verified. Aims. We aim to understand whether
photospheric velocity swirls exist co-spatially and co-temporally with
photospheric magnetic swirls, in order to demonstrate the link between swirls
and pulses. Methods. The automated swirl detection algorithm (ASDA) is applied
to the photospheric horizontal velocity and vertical magnetic fields obtained
from a series of realistic numerical simulations using the RMHD code Bifrost.
The spatial relationship between the detected velocity and magnetic swirls is
further investigated via a well-defined correlation index (CI) study. Results.
On average, there are ~63 short-lived photospheric velocity swirls (with
lifetimes mostly less than 20 s, and average radius of ~37 km and rotating
speeds of ~2.5 km/s) detected in a field of view (FOV) of 6\times6 Mm^{-2},
implying a total population of velocity swirls of ~1.06\times10^7 in the solar
photosphere. More than 80% of the detected velocity swirls are found to be
accompanied by local magnetic concentrations in intergranular lanes. On
average, ~71% of the detected velocity swirls have been found to co-exist with
photospheric magnetic swirls with the same rotating direction. Conclusions. The
co-temporal and co-spatial rotation in the photospheric velocity and magnetic
fields provide evidence that the conjectured condition for the excitation of
Alfv\'en pulses by photospheric swirls is fulfilled.
