Spectrum of Fractal Dimension d(h) for Velocity Increment in Isotropic Turbulence

Abstract

The multifractal nature of isotropic turbulence is revealed from the viewpoint of the d(h) spectrum for longitudinal velocity increment presumed by Frisch and Parisi, using the 3D binomial Cantor set model. The correctly applied Kolmogorov refined similarity hypothesis is found to play a vital role in construction of the rational d(h) spectrum in the entire range of h from the knowledge of the f(α) spectrum for three-dimensional dissipation field of turbulence. It is also shown that velocity increment is not scale-similar in a strict sense, in contrast to dissipation field averaged over the domain across which velocity increment is considered.