Asymptotic Probability Distribution Function Of Longitudinal Velocity Increment In Incompressible Three-Dimensional Turbulence

We investigated the asymptotic probability distribution function of the longitudinal velocity increment in incompressible three-dimensional turbulence. According to the observation on the large Reynolds number atmospheric flow by Praskovsky and Oncley [Phys. Rev. Lett. 73 (1994) 3399] the distribution is of exponential type in the inertial region, whose slope decreases as the separation decreases. This simple nature was examined with the aid of the forced large-scale simulation with R-lambda = 380 on 1024(3) meshes, where a certain embryo of the exponential distribution is found. The deduced asymptotic distribution function agrees quantitatively with the observed pdf by those authors. A possible reason for the exponential distribution is theoretically considered based on the conditional average method.