Inverse statistics and multifractality of exit distances in 3D fully developed turbulence

The inverse structure functions of exit distances have been introduced as a novel diagnostic of turbulence which emphasizes the more laminar regions [1], [2], [3] and [4]. Using Taylor’s frozen field hypothesis, we investigate the statistical properties of the exit distances of empirical 3D fully developed turbulence. We find that the probability density functions of exit distances at different velocity thresholds δvδv can be approximated by stretched exponentials with exponents varying with the velocity thresholds below a critical threshold. We show that the inverse structure functions exhibit clear extended self-similarity (ESS). The ESS exponents ξ(p,2)ξ(p,2) for small pp (p<3.5p<3.5) are well described by ξ(p,2)=p/2ξ(p,2)=p/2, which derives from the observed approximate universality of the distributions of the exit distances for different velocity thresholds δvδv. The data is not sufficient to reject the hypothesis that monofractal ESS is sufficient to explain the data. In contrast, a measure taking into account the dependence between successive exit distances at a given velocity threshold exhibits clear multifractality with negative dimensions, suggesting the existence of a non-trivial dependence in the time series of exit times.