Multifractal Analysis of Turbulence and Granular Flow

The probability density function of velocity fluctuations of granular turbulence (granulence) observed by Radjai and Roux in their two-dimensional simulation of a slow granular flow under homogeneous quasi-static shearing is studied by multifractal analysis (MFA) proposed by the authors. MFA is a unified self-consistent approach for the systems with large deviations, which has been constructed based on the Tsallis-type distribution function that provides an extremum of the extensive Rény or the non-extensive Tsallis entropy under appropriate constraints. It is shown by the present precise analysis that the system of granulence and of turbulence indeed have common scaling characteristics as was pointed out by Radjai and Roux.