Abstract
Recent experiments in high Reynolds number pipe flow have shown the apparent obfuscation of the \(k_x^{-1}\) behaviour in spectra of streamwise velocity fluctuations (Rosenberg et al. in J Fluid Mech 731:46–63, 2013). These data are further analysed here from the perspective of the \(\log r\) behaviour in second-order structure functions, which have been suggested as a more robust diagnostic to assess scaling behaviour. A detailed comparison between pipe flows and boundary layers at friction Reynolds numbers of \({{Re}}_\tau \approx\) 5000–20,000 reveals subtle differences. In particular, the \(\log r\) slope of the pipe flow structure function decreases with increasing wall distance, departing from the expected \(2A_1\) slope in a manner that is different to boundary layers. Here, \(A_1 \approx 1.25\), the slope of the log law in the streamwise turbulence intensity profile at high Reynolds numbers. Nevertheless, the structure functions for both flows recover the \(2A_1\) slope in the log layer sufficiently close to the wall, provided the Reynolds number is also high enough to remain in the log layer. This universality is further confirmed in very high Reynolds number data from measurements in the neutrally stratified atmospheric surface layer. A simple model that accounts for the ‘crowding’ effect near the pipe axis is proposed in order to interpret the aforementioned differences.
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Acknowledgments
The authors wish to thank the Australian Research Council and ONR under Grant N00014-09-1-0263 (Program Manager: Ronald Joslin) for the financial support of this research. We also gratefully acknowledge Professor Detlef Lohse for helpful discussions regarding the need for geometrical corrections in pipe flow.
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This article belongs to a Topical Collection of articles entitled Extreme Flow Workshop 2014. Guest editors: I. Marusic and B. J. McKeon.
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Chung, D., Marusic, I., Monty, J.P. et al. On the universality of inertial energy in the log layer of turbulent boundary layer and pipe flows . Exp Fluids 56, 141 (2015). https://doi.org/10.1007/s00348-015-1994-7
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DOI: https://doi.org/10.1007/s00348-015-1994-7