Scaling of High-Order Statistics in Turbulent Pipe Flow

Direct numerical simulations of turbulent pipe flow involving friction Reynolds numbers of \(Re_\tau \)=180,360,720,1500 were carried out and investigated in terms of high-order statistics. A logarithmic dependency on the Reynolds number was found for the streamwise Reynolds stress where \(Re_\tau \ge 360\), the streamwise skewness and the wall-normal flatness for \(Re_\tau \ge 360\). The scaling failure of the latter quantities is related to large-scale outer flow motions that become important at high Reynolds number flow and penetrate into the near-wall region. For the lowest Reynolds number \(Re_\tau =180\) the streamwise Reynolds stress peak and the wall-normal flatness at the wall exhibited discrepancies to values obtained from channel flow simulations, which can be explained by the different flow geometry interacting with the wall structures that are of large size compared with the geometry at such low Re.