  The Sun features on its surface typical flow patterns called the granulation,
mesogranulation, and supergranulation. These patterns arise due to convective
flows transporting energy from the interior of the Sun to its surface. In this
paper we will shed light on the interaction between the convective flows in
large-scale cells as well as the large-scale magnetic fields in active regions,
and investigate in detail the statistical distribution of flow velocities
during the evolution and formation of National Oceanic and Atmospheric
Administration (NOAA) active region 11190. To do so, we employed local
correlation tracking methods on data obtained by the Solar Dynamics Observatory
(SDO) spacecraft in the continuum as well as on processed line-of-sight (LOS)
magnetograms. We find that the flow fields in an active region can be modelled
by a two-component distribution. One component is very stable, follows a
Rayleigh distribution, and can be assigned to the background flows, whilst the
other component is variable in strength and velocity range and can be
attributed to the flux emergence visible both in the continuum maps as well as
magnetograms. Generally, the plasma flows, as seen by the distribution of the
magnitude of the velocity, follow a Rayleigh distribution even through the time
of formation of active regions. However, at certain moments of large-scale fast
flux emergence, a second component featuring higher velocities is formed in the
velocity magnitudes distribution. The plasma flows are generally highly
correlated to the motion of magnetic elements and vice versa except during the
times of fast magnetic flux emergence as observed by rising magnetic elements.
At these times, the magnetic fields are found to move faster than the
corresponding plasma.
