Temporal characteristics of the probability density function of velocity in wall-bounded turbulent flows
The probability density function (p.d.f.) of the streamwise velocity has been shown to indicate the presence of uniform momentum zones in wall-bounded turbulent flows. Most studies on the topic have focused on the instantaneous characteristics of this p.d.f. In this work, we show how the use of time-resolved particle image velocimetry data highlights robust features in the temporal behaviour of the p.d.f. and how these patterns are associated with the change of the number of zones present in the flow over time. The use of a limited resolvent model provides a clear link between this experimentally observed behaviour and the underlying velocity structures and their phase characteristics. This link is further supported by an extended resolvent model consisting of self-similar hierarchies centred in the logarithmic region, with triadically consistent members, yielding much more complex patterns in the p.d.f. Results indicate that the geometric similarity of these members instantaneously, as well as their relative evolution in time (dictated by their wall-normal varying wave speed), both inherent to the model, can reproduce many experimentally identified features.
© The Author(s), 2021. Published by Cambridge University Press. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited. Received 15 May 2020; revised 17 December 2020; accepted 20 December 2020; Published online by Cambridge University Press: 22 February 2021. The experimental dataset used in this study was acquired by the corresponding author as part of her doctoral degree in the University of Southampton, under the supervision of Professor B. Ganapathisubramani and Professor R. de Kat, both of whom are gratefully acknowledged. The support of the Office of Naval Research under award N00014-17-1-3022 is gratefully acknowledged. The authors report no conflict of interest.
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