Probability Density Function of Longitudinal Velocity Increment in   Homogeneous Turbulence
  Two conditional averages for the longitudinal velocity increment u_r of the simulated turbulence are calculated: h(u_r) is the average of the increment of the longitudinal Laplacian velocity field with u_r fixed, while g(u_r) is the corresponding one of the square of the difference of the gradient of the velocity field. Based on the physical argument, we suggest the formulae for h and g, which are quite satisfactorily fitted to the 512^3 DNS data. The predicted PDF is characterized as   (1) the Gaussian distribution for the small amplitudes,   (2) the exponential distribution for the large ones, and (3) a prefactor before the exponential function for the intermediate ones. 
Naoya Takahashi, Tsutomu Kambe, Tohru Nakano, Toshiyuki Gotoh, and   Kiyoshi Yamamoto