NEGATIVE DIMENSIONS OF THE TURBULENT DISSIPATION FIELD

Random multifractals that involve ensemble-averaged partition sums may give rise to negative dimensions. These models are highly relevant fo r interpreting fluctuations in fully developed hydrodynamic turbulence . From the experimental results that are obtained in a laboratory turb ulent flow, it appears that self-similarity of the partition sums is o nly reached asymptotically. We demonstrate that this effect is due to correlations between subsequent refinements in a multifractal descript ion. We give a way of correcting for the effects of correlations. We a nalyze an exactly solvable model that has the correlation depth as a p arameter. This model has asymptotic self-similarity and displays a pha se transition behavior in the limit of infinite deterministic refineme nts.