  Supersonic turbulence plays a pivotal role during the formation of molecular
clouds and stars in galaxies. However, little is known about how the fraction
of compressive and solenoidal modes in the velocity field evolves over time and
how it depends on properties of the molecular cloud or the galactic
environment. In this work, we carry out magnetohydrodynamical simulations of
disc galaxies and study the time evolution of the turbulence driving parameter
for an ensemble of clouds. We find that the time-averaged turbulence driving
parameter is insensitive to the position of the cloud within the galaxy. The
ensemble-averaged driving parameter is found to be rather compressive with
$b\sim0.5-0.7$, indicating almost time-independent global star formation
properties. However, each individual cloud shows a highly fluctuating driving
parameter, which would strongly affect the cloud's star formation rate. We find
that the mode of turbulence driving can rapidly change within only a few Myr,
both from solenoidal to compressive and vice versa. We attribute these changes
to cloud collisions and to tidal interactions with clouds or overdensities in
the environment. Last, we find no significant differences in the average
driving parameter between hydrodynamic and initially strongly magnetised
galaxies. However, the magnetic field tends to reduce the overall fluctuation
of the driving parameter. The average driving as well as its uncertainty are
seen to be in agreement with recent constraints on the turbulence driving mode
for solar neighbourhood clouds.
