Degeneracy of velocity strain-rate tensor statistics in random isotropic incompressible flows

The article considers the strain-rate tensor distribution in various isotropically distributed incompressible flows. By means of a fortunate choice of variables, a strong degeneracy in the probability distribution of strain-rate tensor characteristics is found in numerical simulations of isotropic turbulence. This allows us to reduce the probability density function (PDF) of the strain-rate tensor to a function of one variable. Also it appears that for those particular parameters that reflect the ratio of different eigenvalues of the strain tensor (s and beta parameters), the shapes of their probability distributions are universal and do not depend on the specific shape of distribution. Furthermore, it is also shown analytically that for all time-reversible statistical isotropic flows the probability distribution of s is uniform, which generalizes previous numerical calculations.