  We report and analyse the results of extensive discrete element method
simulations of three-dimensional gravity driven flows of cohesionless granular
media over an erodible bed, the whole being confined between two flat and
frictional sidewalls. We focus on the role of sidewalls by performing
simulations for different gap widths ($W$) between the two confining sidewalls:
from $5$ to $30$ grain sizes ($d$). Our results indicate the existence of two
distinct regimes: regime I for flow angles smaller than the critical angle
$\theta_c\approx 40^\circ$ and regime II at flow angles larger than $\theta_c$
. Regime I corresponds to dense flows whereas flows belonging to regime II
exhibit a strong variation of the volume fraction through the depth. Three
relevant lengths are identified in the system: $W$ the gap between sidewalls,
$l$ the length characterizing the vertical variation of the volume fraction and
$h$ a characteristic length associated with the vertical variation of the
streamwise velocity. Using these lengths we can rescale the profiles of various
flow properties (e.g. streamwise velocity, granular temperature, particle
rotation...). In regime II, in contrast to regime I, $l$ and $h$ have a similar
behaviour. As a consequence, the rescaled profiles in regime II only involve
$h$ (or equivalently $l$) and $W$ . Other dissimilarities exist between regimes
I and II. In particular, the scaling of the flow rate with $h$ (at fixed $W$ )
differs in the two regimes, although they display a similar scaling with $W$
(at fixed flow angle).
