Quantitative evaluation of nonlinear diffusion for isotropic random flow

The projection operator method is applied to isotropic random flow field. This application derives a model of a time correlation function with no assumption, and allows for quantitative evaluations of the nonlinear diffusion near initial time. We confirm that for wide range of Reynolds number, the model exhibits good agreement with the results calculated by the direct numerical simulation near the initial time. It is concluded that the projection operator method is useful to exhibit quantitatively the dependence of the nonlinear diffusion on the Reynolds number.