Multifractality of Inverse Statistics 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 [1-4]. 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 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 \xi(p,2) for small p (p