Numerical study of granular turbulence and the appearance of the energy spectrum without flow

Abstract

The vibrated bed of powder, a vessel that mono disperse glass beads fill and a loud speaker shakes, is investigated numerically with the distinct element method, a kind of molecular dynamics. When the bed is heavily shaken, the displacement vectors of powder have the power spectrum with the dependence upon the wave number k as k −5/3 . The origin of this spectrum is suggested to be the balance between the injected and dissipative energy, analogous to the proposal by Kolmogorov to explain the k −5/3 energy spectrum observed in the fluid turbulence. Furthermore, the same spectrum still appears even without flows of powder. Thus Kolmogorov's argument is more universal than believed before.

Dynamical simulation of fluidized beds: Hydrodynamically interacting granular particles

“…We briefly explain the relationship between our observed spectra and Kolmogorov scaling. In this sense, our paper has confirmed the universality of the powder turbulence proposed by Taguchi [39].…”

“…Next we discuss the power spectra obtained from the data, which suggest the existence of tails obeying power laws. These power law tails may correspond to those reported by Taguchi [38], and taken as an evidence for powder turbulence [39].…”

Hydrodynamic Description of Granular Convection

“…For finite system, σ ef f (0) = −2π 7 T e /( R2 L 6 ) < 0. Thus, the convection will disappear for infinite systems, which agrees with MD simulations [1,3,15]. Equivalently, convection also disappears in the limit of large R, i.e.…”