Inter-scale interaction in pipe flows at high Reynolds numbers

Hot-wire measurements of the streamwise velocity are conducted in the large-scale pipe-flow facility CICLoPE in the friction Reynolds number range of 7800⩽Reτ<40000. Measurements are performed both with a rake of five synchronised probes arranged at different radial locations, and through a radial scan with a single wire traversing the whole pipe radius. Correlation-based analysis is used to extract features of inter-scale modulation in turbulent pipe flows. The Reτ-independence of geometric features is shown with the outer scaling. Very-large-scale motions keep the vertical coherence to the wall through the whole pipe radius, while for the large-scale motions, the local coherence gradually become isotropic as the structure centre moves far away from the wall. From results obtained with the one-point amplitude modulation (AM) correlation function map, the AM effect is characterised by positive correlations observed in the inner region, while an opposite AM effect characterised by negative correlations is observed in the outer region. The strongest AM effect (with the maximum correlations) and the zero net-modulation (with zero correlations) show that the phase difference between large and small scales has a linear relation with the logarithm of the outer-scaled wall distance, but the strongest opposite effect (with the negative maximum correlations) behaves with the phase difference independent of the outer scaled wall-normal distance. Two-point AM coefficient maps, which give richer spatial information in the outer region than the one-point map, present the Reτ-independence for AM and opposite effects within the present Reτ range. In addition, the relative variation of the two effects in the coexisting wall-normal range is characterised by identifying the maximum gradient of the one-point AM coefficient and the peak-to-peak value of the two-point AM coefficient map.