Convergence of numerical simulations of turbulent wall-bounded flows and mean cross-flow structure of rectangular ducts

Convergence criteria for direct numerical simulations of turbulent channel and duct flows are proposed. The convergence indicator for channels is defined as the deviation of the nondimensional total shear-stress profile with respect to a linear profile, whereas the one for the duct is based on a nondimensional streamwise momentum balance at the duct centerplane. We identify the starting () and averaging times () necessary to obtain sufficiently converged statistics, and also find that optimum convergence rates are achieved when the spacing in time between individual realizations is below . The in-plane structure of the flow in turbulent ducts is also assessed by analyzing square ducts at and 360 and rectangular ducts with aspect ratios 3 and 10 at . Identification of coherent vortices shows that near-wall streaks are located in all the duct cases at a wall-normal distance of as in Pinelli et al. (J Fluid Mech 644:107-122, 2010). We also find that large-scale motions play a crucial role in the streamline pattern of the secondary flow, whereas near-wall structures highly influence the streamwise vorticity pattern. These conclusions extend the findings by Pinelli et al. to other kinds of large-scale motions in the flow through the consideration of wider ducts. They also highlight the complex and multiscale nature of the secondary flow of second kind in turbulent duct flows.