The experimental study on the turbulent statistics in the outer layer in high Reynolds number turbulent pipe flow

Turbulent statistical properties in the outer region are presented for high Reynolds number turbulent pipe flow using LDV (Laser Doppler Velocimetry) measurement. Employing the indicator function for turbulence intensity, the region which has logarithmic behavior is not only observed in second moment but also higher even moments. It is found that power spectrum density distributions in these regions have approximately -1 law profile which mainly consists of LSM (Large Scale Motion) and VLSM (Very Large Scale Motion). However, the spectral dependence on the wall distance is different from based on Attached-Eddy model. We observed that the region where PDFs (Probability Density Function) are approximately invariant against the wall normal distance is enlarged with increasing Reynolds number. And, it is found that this invariant PDF region overlaps with logarithmic profiles of the even order moments. We clarified the relation between logarithmic behaviors in the even order moments and invariance property of PDF against the wall distance. However, in the finite Reynolds number experiment, it is reported that invariance property of PDF is approximately satisfied. And so, we derived the relation between the even moment profiles and invariance of PDF, and verified the relation using experimental results. Finally, we expected that, in the infinite Reynolds number condition, the invariance property of PDF and the logarithmic relations in the even moments are realized.