Fractional and fractal derivatives modeling of turbulence

Details Fractional and fractal derivatives modeling of turbulence Fractional and fractal derivatives modeling of turbulence

2005-11-30

arxiv.org/abs/nlin/0511066v1

Nonlinear Sciences

Chaotic Dynamics

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Scientific paper

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.

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