Direct numerical simulation of turbulent pipe flow at Re_tau=10,000

A new DNS of a (smooth-wall) turbulent pipe flow has been performed for a friction Reynolds number of 10,000 -- larger than previous simulations available in the literature. Given the excessive computational resources necessary, we limited the pipe length to 2 pi R, where R is the pipe radius. This length similar as in comparable recent channel simulations at high Reynolds numbers. The discretization is based on accurate high-order spectral/finite-difference approximations where special care has be put onto resolving the near-wall region. Various low and high-order turbulence statistics are compared with other DNS and experimental data in pipes as well as channels and other canonical flows, as available. Of particular interest is the log-law indicator function, which is shown to be nearly indistinguishable between the pipe and channel up to y+=250. Farther away from the wall, it develops a plateau, with a kappa=0.384, similar to other canonical turbulent wall-bounded cases. Given the new data for the mean flow, we will assess different composite profiles, asymptotic expansions and data-fitting approaches, and discuss some of the commonly employed corrections. Using the fluctuation field, we will also look at spectra to understand the energy distribution as compared to channels. Finally, we will also quantify the uncertainty in the data using an auto-regressive approximation.