Anisotropic homogeneous turbulence: Hierarchy and intermittency of scalingexponents in the anisotropic sectors

We present the first measurements of anisotropic statistical fluctuations i n perfectly homogeneous turbulent flows. We address both problems of interm ittency in anisotropic sectors and hierarchical ordering of anisotropies on a direct numerical simulation of a three dimensional random Kolmogorov flo w. We achieved an homogeneous and anisotropic statistical ensemble by rando mly shifting the forcing phases. We observe high intermittency as a functio n of the order of the velocity correlation within each fixed anisotropic se ctor and a hierarchical organization of scaling exponents at fixed order of the velocity correlation at changing the anisotropic sector.