Pressure and spanwise velocity fluctuations in turbulent channel flows: Logarithmic behavior of moments and coherent structures

We study the logarithmic behavior of the pressure variance (p+2) from the datasets obtained from direct numerical simulations of turbulent channel flow for friction Reynolds number Reτ up to 4000. The higher-order moments of p were found to follow logarithmic behaviors at the same distances from the wall where (p+2) shows its log profile. The same results have been confirmed for the spanwise velocity fluctuations w at the same Reynolds numbers, with both p and w following a super-Gaussian behavior. The minimum Reynolds number for (p+2) and (w+2) log profiles to appear is Reτ≈500, where flow structures O(h) or less were found to significantly contribute to these profiles. The configuration of the hairpin eddy structures obtained from the conditional sampling at different wall-normal locations showed a strong link between p and w fluctuations. Positive pressure fluctuations are located between the legs of the hairpin eddy, while the negative pressure fluctuations are consistent with the head part of the hairpin eddy. Positive and negative spanwise velocity fluctuations are strongly positioned with the legs of the hairpin eddy, consistent with the counter-rotating motion resulting from the eddy legs. The structures were also found to be geometrically self-similar such that their length and their width increase linearly with the distance from the wall.