Fractal Dimension of Velocity Signals in High Reynolds-Number Hydrodynamic Turbulence

A. Scotti, C. Meneveau
Department of Mechanical Engineering
The Johns Hopkins University | Baltimore, MD 21218

S. G. Saddoughi
Center for Turbulence Research | Stanford, CA 94305

ABSTRACT: In this paper the fractal nature of velocity signals as measured in turbulent flows is investigated. In particular, we study the geometrical nature of the graph (x,f(x)) of the function f that gives one component of the velocity at position x. Special emphasis is given to the effects that a limited resolution of the signal, or natural small-scale cut offs, have on the estimate of the fractal dimension, and a new procedure to account for such finite-size effects is proposed and tested on artificial fractal graphs. We then consider experimental data from three turbulent flows: the wake behind a circular cylinder, the atmospheric surface layer and the rough-wall zero-pressure-gradient boundary layer developing on the test-section ceiling of the 80'x120' full-scale NASA Ames wind tunnel (the world's largest wind tunnel). The results clearly indicate that at high Reynolds number, turbulent velocity signals have a fractal dimension of D~1.7±0.05, very near the value of D=5/3 expected for Gaussian processes with a -5/3 power-law in their power spectrum.

Phys. Rev. E, 51, 5594–5608

DOI: 10.1103/PhysRevE.51.5594 | Full PDF
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