  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.
