Geometrical Statistics in Turbulence

Abstract

Geometrical invariant quantities (such as enstropy generation, helicity, etc.) and relations (such as alignments between various vectors) - being independent of the frame of reference - are among the most appropriate for studying physical processes and characterization of the structure of turbulent flows. Moreover, just like phase relations these are the quantities and relations of utmost dynamical significance. An overview of a variety of alignments is given below along with applications to basic issues¹ with the emphasis on the physical aspects on the basis of both laboratory and numerical experiments.^{2, 3}