Pseudo-Gauss distribution: a reversible counterpart of the true turbulent velocity gradient distribution

On the grounds of both widely known experimental and numerical data of the strain-rate tensor statistical properties in the fully developed incompressible turbulent flow and the integral transformations deduced in the article, some important statistical properties of the flow, known as kinematical, are found to be dynamical (i.e. taking place purely in a turbulent flow). A new pseudo-Gauss distribution is introduced in the article and, as a consequence of these properties, a considerable feature distinguishing this distribution from the Gauss one is found to be the general feature of the turbulent statistics. Thus, the new distribution is proved to be a reversible counterpart of the true turbulent velocity gradient distribution instead of the Gauss one.