Kolmogorov 1941 theory is based, among others, on the idea of
universality of the statistical properties and restoration of isotropy
at small scale in turbulent flows. Recently many
theoretical, numerical and experimental works seem to point in the
opposite direction talking explicitly of  persistence of anisotropy.
Typical questions go from the theoretical point of calculating and
measuring anomalous scaling exponents in anisotropic sectors,
to the more applied problem of quantifying the rate of recovery of isotropy at small scales.
We decided to investigate the issue by means of 3D direct numerical simulations (DNS) of a
perfectly homogeneous and anisotropic flow.
In particular we performed DNS of a ``Random Kolmogorov Flow'', i.e. a flow
where only one component of the velocity is forced, v_z, at two
wavenumbers (say k_1=(1,0,0) and k_2=(2,0,0)).
We give a new argument to predict the dimensional scaling exponents, zeta^j_d(p) =
(p+j)/3, for the projections of the p-th order structure function
in the j-th sector of the rotational group. We show that the
measured exponents are anomalous, showing a clear deviation from the
dimensional prediction. Dimensional scaling is subleading and
connected to the dynamical fluctuations without phase correlations.
Universality of the observed anomalous scaling is discussed both
theoretically and by mean of numerical simulations at different
Reynolds numbers and with different forcing.
Finally, perspectives and open questions of the present work will be sketched.