On the universality of inertial energy in the log layer of turbulent boundary layer and pipe flows

On the universality of inertial energy in the log layer of turbulent boundary layer and pipe flows Recent experiments in high Reynolds number pipe flow have shown the apparent obfuscation of the $$k_x^{-1}$$ 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 $$\log r$$ 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 $${{Re}}_\tau \approx$$ R e τ ≈  5000–20,000 reveals subtle differences. In particular, the $$\log r$$ log r slope of the pipe flow structure function decreases with increasing wall distance, departing from the expected $$2A_1$$ 2 A 1 slope in a manner that is different to boundary layers. Here, $$A_1 \approx 1.25$$ A 1 ≈ 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 $$2A_1$$ 2 A 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Experiments in Fluids Springer Journals

On the universality of inertial energy in the log layer of turbulent boundary layer and pipe flows

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2015 by Springer-Verlag Berlin Heidelberg
Subject
Engineering; Engineering Fluid Dynamics; Fluid- and Aerodynamics; Engineering Thermodynamics, Heat and Mass Transfer
ISSN
0723-4864
eISSN
1432-1114
D.O.I.
10.1007/s00348-015-1994-7
Publisher site
See Article on Publisher Site

Abstract

Recent experiments in high Reynolds number pipe flow have shown the apparent obfuscation of the $$k_x^{-1}$$ 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 $$\log r$$ 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 $${{Re}}_\tau \approx$$ R e τ ≈  5000–20,000 reveals subtle differences. In particular, the $$\log r$$ log r slope of the pipe flow structure function decreases with increasing wall distance, departing from the expected $$2A_1$$ 2 A 1 slope in a manner that is different to boundary layers. Here, $$A_1 \approx 1.25$$ A 1 ≈ 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 $$2A_1$$ 2 A 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.

Journal

Experiments in FluidsSpringer Journals

Published: Jun 25, 2015

References

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