  Turbulence is ubiquitous in nonequilibrium systems, and it has been noted
that even dense granular flows exhibit characteristics that are typical of
turbulent flow, such as the power-law energy spectrum. However, studies on the
turbulent-like behavior of granular flows are limited to two-dimensional (2D)
flow. We demonstrate that the statistics in three-dimensional (3D) flow are
qualitatively different from those in 2D flow. We also elucidate that avalanche
dynamics can explain this dimensionality dependence. Moreover, we define
clusters of collectively moving particles that are equivalent to vortex
filaments. The clusters unveil complicated structures in 3D flows that are
absent in 2D flows.
