Theoretical and numerical study of highly anisotropic turbulent flows

We present a detailed numerical study of anisotropic statistical fluctuations in stationary, homogeneous turbulent flows. We address both problems of intermittency in anisotropic sectors, and the relative importance of isotropic and anisotropic fluctuations at different scales on a direct numerical simulation of a three-dimensional random Kolmogorov flow. We review a simple argument to predict the dimensional scaling for all velocity moments, in all anisotropic sectors. We extend a previous analysis made on the same data set (Phys. Rev. Lett. 86 (2001) 4831) presenting (i) the statistical behavior of spectra and co-spectra; (ii) high-order longitudinal structure functions; (iii) anisotropic fluctuations of the full tensorial two-points velocity correlations. Among the many issues discussed, we stress the problem of the return-to-isotropy, the universality of anisotropic fluctuations and the foliation mechanism. A new a priori test on sub-grid quantities used in Large-Eddy Simulations is also presented.