Negative dimensions of the turbulent dissipation field

J. Molenaar, J.A. Herweijer, W. Water, van de

Research output: Contribution to journalArticleAcademicpeer-review

13 Citations (Scopus)


Random multifractals that involve ensemble-averaged partition sums may give rise to negative dimensions. These models are highly relevant for interpreting fluctuations in fully developed hydrodynamic turbulence. From the experimental results that are obtained in a laboratory turbulent flow, it appears that self-similarity of the partition sums is only reached asymptotically. We demonstrate that this effect is due to correlations between subsequent refinements in a multifractal description. We give a way of correcting for the effects of correlations. We analyze an exactly solvable model that has the correlation depth as a parameter. This model has asymptotic self-similarity and displays a phase transition behavior in the limit of infinite deterministic refinements.
Original languageEnglish
Pages (from-to)496-509
Number of pages14
JournalPhysical Review E: Statistical, Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Issue number1
Publication statusPublished - 1995


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