SINGULARITY SPECTRUM OF THE VELOCITY INCREMENT IN ISOTROPIC TURBULENCE

A reasonable picture of the singularity spectrum d(h) of the longitudinal velocity increment presumed by Frisch and Parisi is given. The Kolmogorov refined similarity hypothesis is found to play a vital role in constructing the d(h) spectrum in the entire range of h from the knowledge of the f(α) spectrum for the three-dimensional dissipation field of turbulence. The feature of d(h) obtained for the lognormal model is discussed in comparison with other models. Although the lognormal model itself is now known not to be the best one, it is typical in that it is analytically treated without a numerical process and it has a universal tendency, at least, in the right branch of d(h). © 1995 The American Physical Society.