Quantifying uncertainties in direct-numerical-simulation statistics due to wall-normal numerics and grids

This paper takes the perspective of a user of direct-numerical-simulation (DNS) data and quantifies the uncertainties in DNS statistics for plane channel flows. We focus on high-order statistics, such as skewness, kurtosis, and viscous dissipation, and quantify the uncertainties due to wall-normal numerics and grids while minimizing the sampling error and the discretization error in the wall-parallel directions. Two grid distributions and four discretization methods are considered, which are representative of the existing DNSs. Our results show that the available DNS data contain at least a 7% uncertainty in the computed mean viscous dissipation in the buffer layer. Moreover, since turbulence becomes more intermittent at higher Reynolds numbers, the flow will be less well-resolved at the higher Reynolds number if the same grid resolution in terms of the viscous units is employed. Specifically, our estimate shows that a grid that resolves 90% of the dissipation events at Reτ=544 resolves about 87% of the dissipation events at Reτ=10000.