Context. Observations show that small-scale vortical plasma motions are ubiquitous in the quiet solar atmosphere. They have received increasing attention in recent years because they are a viable candidate mechanism for the heating of the outer solar atmospheric layers. However, the true nature and the origin of these swirls, and their effective role in the energy transport, are still unclear.Aims. We investigate the evolution and origin of chromospheric swirls by analyzing numerical simulations of the quiet solar atmosphere. In particular, we are interested in finding their relation with magnetic field perturbations and in the processes driving their evolution.Methods. The radiative magnetohydrodynamic code CO5BOLD is used to perform realistic numerical simulations of a small portion of the solar atmosphere, ranging from the top layers of the convection zone to the middle chromosphere. For the analysis, the swirling strength criterion and its evolution equation are applied in order to identify vortical motions and to study their dynamics. As a new criterion, we introduce the magnetic swirling strength, which allows us to recognize torsional perturbations in the magnetic field.Results. We find a strong correlation between swirling strength and magnetic swirling strength, in particular in intense magnetic flux concentrations, which suggests a tight relation between vortical motions and torsional magnetic field perturbations. Furthermore, we find that swirls propagate upward with the local Alfven speed as unidirectional swirls driven by magnetic tension forces alone. In the photosphere and low chromosphere, the rotation of the plasma co-occurs with a twist in the upwardly directed magnetic field that is in the opposite direction of the plasma flow. All together, these are clear characteristics of torsional Alfven waves. Yet, the Alfven wave is not oscillatory but takes the form of a unidirectional pulse. The novelty of the present work is that these Alfven pulses naturally emerge from realistic numerical simulations of the solar atmosphere. We also find indications of an imbalance between the hydrodynamic and magnetohydrodynamic baroclinic effects being at the origin of the swirls. At the base of the chromosphere, we find a mean net upwardly directed Poynting flux of 12.86.5 kW m(-2), which is mainly due to swirling motions. This energy flux is mostly associated with large and complex swirling structures, which we interpret as the superposition of various small-scale vortices.Conclusions. We conclude that the ubiquitous swirling events observed in numerical simulations are tightly correlated with perturbations of the magnetic field. At photospheric and chromospheric levels, they form Alfven pulses that propagate upward and may contribute to chromospheric heating.