ABSTRACT
In the last decade it has been shown by the present authors and co-workers, that all of the complete statistical approaches of turbulence based on Navier-Stokes equations i.e. the infinite set of multi-point moment equations, the infinite hierarchy of multi-point probability-density function equations and the Hopf functional equation admit more symmetries compared to the original Navier-Stokes equations. Hence, these equations admit symmetries which go beyond the classical Galilean group of Navier-Stokes equations, and were named statistical symmetries. For the generic three-dimensional case these symmetries mirror important properties such as intermittency and non-gaussianity. The above findings are important consequences for our understanding of the statistics of turbulence such as intermittency and non-gaussianity.
