  It was recently observed that sand flowing down a vertical tube sometimes
forms a traveling density pattern in which a number of regions with high
density are separated from each other by regions of low density. In this work,
we consider this behavior from the point of view of kinetic wave theory.
Similar density patterns are found in molecular dynamic simulations of the
system, and a well defined relationship is observed between local flux and
local density -- a strong indicator of the presence of kinetic waves. The
equations of motion for this system are also presented, and they allow kinetic
wave solutions. Finally, the pattern formation process is investigated using a
simple model of interacting kinetic waves.
