  This study makes the first attempt to use the 2/3-order fractional Laplacian
modeling of enhanced diffusing movements of random turbulent particle resulting
from nonlinear inertial interactions. A combined effect of the inertial
interactions and the molecule Brownian diffusivities is found to be the
bi-fractal mechanism behind multifractal scaling in the inertial range of
scales of moderate Reynolds number turbulence. Accordingly, a stochastic
equation is proposed to describe turbulence intermittency. The 2/3-order
fractional Laplacian representation is also used to construct a fractional
Reynolds equation for nonlinear interactions of fluctuating velocity
components, underlying turbulence spacetime fractal structures of Levy 2/3
stable distribution. The new perspective of this study is that the fractional
calculus is an effective approach modeling of chaotic fractal phenomena induced
by nonlinear interactions.
