some statistics of turbulence are a consequence of so-called ejections/sweeping processes in the near-wall region, brought by the bursting of hairpins, which is the growth of many unstable modes. Some others are due to "outer" motions (coherent structures), with very large modes. These phenomena is inertial, hence resolved by LES. To model these means doing RANS, or it means you have all relevant modes (spectral non-linear scales, via SVD) which you can superpose to your 'steady' solution, from which LES would pick up...