SPECTRUM OF FRACTAL DIMENSION D(H) FOR VELOCITY INCREMENT IN ISOTROPIC TURBULENCE

The multifractal nature of isotropic turbulence is revealed from the v iewpoint of the d(h) spectrum for longitudinal velocity increment pres umed by Frisch and Parisi, using the 3D binomial Cantor set model. The correctly applied Kolmogorov refined similarity hypothesis is found t o play a vital role in construction of the rational d(h) spectrum in t he entire range of h from the knowledge of the f(alpha) spectrum for t hree-dimensional dissipation field of turbulence. It is also shown tha t velocity increment is not scale-similar in a strict sense, in contra st to dissipation field averaged over the domain across which velocity increment is considered.