Velocity Probability Distribution Function in the Crossover and the Viscous Range

We derive a multifractal model for the velocity probability density distribution function (PDF), which is valid from the inertial range to the viscous range. The model gives a continuous evolution of velocity PDFs from large to small scales. It also predicts the asymptotic form of the PDF of velocity gradients. More importantly, the model captures the crossover range behavior and thus allows us to address the transition observed in the Helium turbulence experiment[Tabeling et. al., Phys. Rev. E53, 1613 (1996)] quantitatively. We compare both the PDFs and the structure functions predicted by this model with the experiments from the inertial range to the smallest scale resolved by the experiment. The model also predicts that the flatness measured in the crossover region can decrease with the Reynolds number.