Analysis of accelerations in turbulence based on generalizaed statistics

An analytical expression of probability density function (PDF) of accelerations in turbulence is derived 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 and coworkers in the measurement of fluid particle accelerations in the Lagrangian frame at $R_{\lambda }=970$.