R Benzi1, G Paladin1, G Parisi1 and A Vulpiani1
Published under licence by IOP Publishing Ltd
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Citation R Benzi et al 1984 J. Phys. A: Math. Gen. 17 3521
DOI 10.1088/0305-4470/17/18/021
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It is generally argued that the energy dissipation of three-dimensional turbulent flow is concentrated on a set with non-integer Hausdorff dimension. Recently, in order to explain experimental data, it has been proposed that this set does not possess a global dilatation invariance: it can be considered to be a multifractal set. The authors review the concept of multifractal sets in both turbulent flows and dynamical systems using a generalisation of the beta -model.