Multifractal analysis of fluid particle accelerations in turbulence

The probability density function (PDF) of accelerations in turbulence is derived analytically with the help of the multifractal analysis based on generalized entropy, i.e., the Tsallis or the R\'{e}nyi entropy. It is shown that the derived PDF explains quite well the one obtained by Bodenschatz et al. in the measurement of fluid particle accelerations in the Lagrangian frame at $R_\lambda = 690$, and the one by Gotoh et al. in the DNS with the mesh size 1024$^3$ at $R_\lambda = 380$.