  Using advanced numerical magneto-hydrodynamic simulations of the magnetised
solar photosphere, including non-grey radiative transport and a non-ideal
equation of state, we analyse plasma motions in photospheric magnetic vortices.
We demonstrate that apparent vortex-like motions in photospheric magnetic field
concentrations do not exhibit "tornado"-like behaviour or a "bath-tub" effect.
While at each time instance the velocity field lines in the upper layers of the
solar photosphere show swirls, the test particles moving with the
time-dependent velocity field do not demonstrate such structures. Instead, they
move in a wave-like fashion with rapidly changing and oscillating velocity
field, determined mainly by magnetic tension in the magnetised intergranular
downflows. Using time-distance diagrams, we identify horizontal motions in the
magnetic flux tubes as torsional Alfv\'en perturbations propagating along the
nearly vertical magnetic field lines with local Alfv\'en speed.
