The relationship between vortex flows at different spatial scales and their
contribution to the energy balance in the chromosphere is not yet fully
understood. We perform three-dimensional (3D) radiation-magnetohydrodynamic
(MHD) simulations of a unipolar solar plage region at a spatial resolution of
10 km using the MURaM code. We use the swirling-strength criterion that mainly
detects the smallest vortices present in the simulation data. We additionally
degrade our simulation data to smooth-out the smaller vortices, so that also
the vortices at larger spatial scales can be detected. Vortex flows at various
spatial scales are found in our simulation data for different effective spatial
resolutions. We conclude that the observed large vortices are likely clusters
of much smaller ones that are not yet resolved by observations. We show that
the vertical Poynting flux decreases rapidly with reduced effective spatial
resolutions and is predominantly carried by the horizontal plasma motions
rather than vertical flows. Since the small-scale horizontal motions or the
smaller vortices carry most of the energy, the energy transported by vortices
deduced from low resolution data is grossly underestimated. In full resolution
simulation data, the Poynting flux contribution due to vortices is more than
adequate to compensate for the radiative losses in plage, indicating their
importance for chromospheric heating.Comment: 8 pages, 5 figures, accepted in ApJ
