  We present a numerical study of anisotropic statistical fluctuations in
homogeneous turbulent flows. We give an argument to predict the dimensional
scaling exponents, (p+j)/3, for the projections of p-th order structure
function in the j-th sector of the rotational group. We show that measured
exponents are anomalous, showing a clear deviation from the dimensional
prediction. Dimensional scaling is subleading and it is recovered only after a
random reshuffling of all velocity phases, in the stationary ensemble. This
supports the idea that anomalous scaling is the result of a genuine inertial
evolution, independent of large-scale behavior.

Chaotic Dynamics