  In a recent article (Forterre, PRL, 2001), we have reported a new instability
observed in rapid granular flows down inclined planes that leads to the
spontaneous formation of longitudinal vortices. From the experimental
observations, we have proposed an instability mechanism based on the coupling
between the flow and the granular temperature in rapid granular flows. In order
to investigate the relevance of the proposed mechanism, we perform in the
present paper a three-dimensional linear stability analysis of steady uniform
flows down inclined planes using the kinetic theory of granular flows. We show
that in a wide range of parameters, steady uniform flows are unstable under
transverse perturbations. The structure of the unstable modes are in
qualitative agreement with the experimental observations. This theoretical
analysis shows that the kinetic theory is able to capture the formation of
longitudinal vortices and validates the instability mechanism.
