An analytical solution for probability density function of stretching rate in homogeneous isotropic turbulence

A closed-form expression is derived for the probability density function (pdf) of the stretching rate in homogeneous isotropic turbulence. The pdf has the Reynolds-number-independent Gaussian part and Reynolds-number-dependent non-Gaussian part. The physical meanings of the relevant parameters are discussed, and particularly the Reynolds-number effects on the pdf and statistical quantities are examined.