Inversion formula of multifractal energy dissipation in 3D fully   developed turbulence
  The concept of inverse statistics in turbulence has attracted much attention in the recent years. It is argued that the scaling exponents of the direct structure functions and the inverse structure functions satisfy an inversion formula. This proposition has already been verified by numerical data using the shell model. However, no direct evidence was reported for experimental three dimensional turbulence. We propose to test the inversion formula using experimental data of three dimensional fully developed turbulence by considering the energy dissipation rates in stead of the usual efforts on the structure functions. The moments of the exit distances are shown to exhibit nice multifractality. The inversion formula between the direct and inverse exponents is then verified. 
Jian-Liang Xu (ECUST), Wei-Xing Zhou, Hai-Feng Liu, Xin Gong, Fu-Cheng   Wang, Zun-Hong Yu