On the role of secondary motions in turbulen square duct flow

We use a direct numerical simulations (DNS) database for turbulent flow in a square duct up to bulk Reynolds number Re-b = 40000 to quantitatively analyse the role of secondary motions on the mean flow structure. For that purpose we derive a generalized form of the identity of Fukagata, Iwamoto and Kasagi (FIX), which allows one to quantify the effect of cross-stream convection on the mean streamwise velocity, wall shear stress and bulk friction coefficient. Secondary motions are found to contribute approximately 6% of the total friction, and to act as a self-regulating mechanism of turbulence whereby wall shear stress non-uniformities induced by corners are equalized, and universality of the wall-normal velocity profiles is established. We also carry out numerical experiments whereby the secondary motions arc artificially suppressed, in which case their equalizing role is partially taken by the turbulent stresses.