Two complementary descriptions of intermittency

Abstract

We describe two complementary formalisms designed for the description of probability density function (PDF) of the gradients of turbulent fields. The first approach, we call it adiabatic, describes PDF at the values much less than dispersion. The second, instanton, approach gives the tails of PDF at the values of the gradient much larger than dispersion. Together, both approaches give satisfactory description of gradient PDFs, as illustrated here by an example of a passive scalar advected by a one-dimensional compressible random flow.