  A flow in which a thin film falls due to gravity on the inner surface of a
vertical, rotating cylinder is investigated. This is performed using
two-dimensional (2D) and three-dimensional (3D) direct numerical simulations,
with a volume-of-fluid approach to treat the interface. The problem is
parameterised by the Reynolds, Froude, Weber and Ekman numbers. The variation
of the Ekman number ($Ek$), defined to be proportional of the rotational speed
of the cylinder, has a strong effect on the flow characteristics. Simulations
are conducted over a wide range of $Ek$ values ($0 \leq Ek \leq 484$) in order
to provide detailed insight into how this parameter influences the flow. Our
results indicate that increasing $Ek$, which leads to a rise in the magnitude
of centrifugal forces, produces a stabilising effect, suppressing wave
formation. Key flow features, such as the transition from a 2D to a more
complex 3D wave regime, are influenced significantly by this stabilisation, and
are investigated in detail. Furthermore, the imposed rotation results in
distinct flow characteristics such as the development of angled waves, which
arise due to the combination of gravitationally- and centrifugally-driven
motion in the axial and azimuthal directions, respectively. We also use a
weighted residuals integral boundary layer method to determine a boundary in
the space of Reynolds and Ekman numbers that represents a threshold beyond
which waves have recirculation regions.
