This paper provides insight to the transient development of density waves generated in
gravity-driven flows of granular materials. The evolution of three modes of dominant
linear instabilities (predicted in a previous work by Wang, Jackson & Sundaresan
1997) is examined by FFT analysis. For the first symmetric density wave (SDW1)
mode, the evolution is governed by the linear instability. The second symmetric
density wave (SDW2) mode undergoes a few stages of temporal development; as a
result, large particle clusters gradually degenerate into a series of smaller clusters in
the flow direction. For the anti-symmetric (ASDW) mode, the corresponding particle
distribution shows significant development in the direction perpendicular to the flow.
The present study indicates that the wall roughness may affect the structure of the
density waves, but these density waves need not be triggered by the wall roughness.
All the three modes of instabilities reported in this work are of inertial nature and
occur only when the particle–particle collisions are significantly inelastic.