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Direct numerical simulations of turbulent pipe flow in a flow domain of length L = 42R, friction Reynolds\udnumber in the range of 180 ≤ Reτ ≤ 1500 and two different wall-normal grid refinements were carried out\udand investigated in terms of turbulent high-order statistics. The phenomenology of large local wall-normal\udvelocity fluctuations (velocity spikes) was discussed by means of time series and instantaneous flow-field\udrealisations. Due to their rare appearance both in space and time, statistical high-order moments take\udquite a long time to converge. A convergence study was performed and for fully converged statistics the\udsensitivity of the wall-normal kurtosis component value on the wall as well as the scaling behaviour of high-\udorder statistics was investigated. The streamwise Reynolds stress as well as the streamwise skewness and\udthe wall-normal flatness exhibited logarithmic Reynolds number dependencies in the vicinity of the wall and\udscaling laws were derived accordingly. In the bulk flow region a sudden increase in magnitude in both the\udstreamwise Reynolds stress and skewness was determined for the largest Reynolds number Reτ = 1500, while\udthe profiles scaled well in wall units for Reτ ≤ 720. Both Reynolds number dependencies in the near-wall\udand the bulk region could be related to large-scale outer flow motions penetrating the buffer layer. While\udwavelengths related to larger-scale motions (λz ≈ 3R) were computed for Reynolds numbers up to Reτ = 720\udby means of two-dimensional two-point velocity correlations, even larger wavelengths related to very-large-\udscale motions appeared for Reτ = 1500 and are the probable cause of the sudden increase in magnitude of\udstreamwise Reynolds stress and skewness, respectively. With the aid of instantaneous flow field realisations\udand conditional averaged statistics, the Reynolds dependency of the wall-normal flatness value at the wall\udwas related to the scaling failure of the streamwise Reynolds stress peak. For the lowest Reynolds number\ud(Reτ = 180), discrepancies between plane channel and pipe flow were found and discussed

On the convergence and scaling of high-order statistical moments in turbulent pipe flow using direct numerical simulations