Abstract
The diagnostic plot was introduced in 2010 (Eur. J. Mech. B/Fluids 29: 403–406) but was used already in 2008 during a large measurement campaign as a litmus test to determine if tripped zero-pressure gradient turbulent boundary layers fulfilled basic criteria of being canonical. It used the rms-level of streamwise velocity (\(u_\mathrm {rms}\)) in the outer part of the boundary layer, a region where \(u_\mathrm {rms}\) can give clear indications if insufficient or too tough tripping has been used. In standard plots one needs both the friction velocity and measurement of the full velocity and turbulence profiles. By instead plotting \(u_\mathrm {rms}/U_\infty \) as a function of \(U/U_\infty \), it was found that this gives rise to a well-defined distribution that could be used as a canonical measure. It was later discovered that it is possible to extend the description to the near wall region. It has also been extended to boundary layers over rough surfaces and with pressure gradients, and some further uses. This paper aims to be both a review of the development of the method during the last 10+ years and a tutorial for those who want to employ it in their research and maybe also find new uses of the methodology.
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P.H. Alfredsson, R. Örlü, The diagnostic plot - a litmus test for wall bounded turbulence data. Eur. J. Mech. B/Fluids 29, 403–406 (2010)
P.H. Alfredsson, A. Segalini, R. Örlü, A new scaling for the streamwise turbulence intensity in wall-bounded turbulent flows and what it tells us about the outer peak. Phys. Fluids 23, 041702 (2011)
P.H. Alfredsson, R. Örlü, A. Segalini, A new formulation for the streamwise turbulence intensity distribution in wall-bounded turbulent flows. Eur. J. Mech. B/Fluids 36, 167–175 (2012)
I.P. Castro, A. Segalini, P.H. Alfredsson, Outer layer turbulence intensities in smooth- and rough-wall boundary layers. J. Fluid Mech. 727, 119–131 (2013)
D.B. DeGraaff, J. Eaton, Reynolds-number scaling of the flat-plate turbulent boundary layer. J. Fluid Mech 422, 319–346 (2000)
A. Drózdz, W. Elsner, S. Drobniak, Scaling of streamwise Reynolds stress for turbulent boundary layers with pressure gradient. Eur. J. Mech. B/Fluids 49, 137–145 (2015)
G. Eitel-Amor, R. Örlü, P. Schlatter, Simulation and validation of a spatially evolving turbulent boundary layers up to \(Re_\theta =8300\). Int. J. Heat Fluid Flow 47, 57–69 (2014)
M. Matsubara, P.H. Alfredsson, A. Segalini, Linear modes in a planar turbulent jet. J Fluid Mech 888, A26 (2020)
T. Medjnoun, C. Vanderwel, B. Ganapathisubramani, Characteristics of turbulent boundary layers over smooth surfaces with spanwise heterogeneities. J. Fluid Mech. 838, 516–543 (2018)
M. Metzger, B.J. Mckeon, H. Holmes, The near-neutral atmospheric surface layer: turbulence and non-stationarity. Phil. Trans. R. Soc. A 365, 859–876 (2007)
P.A. Monkewitz, K.A. Chauhan, H.M. Nagib, Self-consistent high-Reynolds number asymptotics for zero-pressure-gradient turbulent boundary layers. Phys. Fluids 19, 115101 (2007)
R. Örlü, Experimental Studies in Jet Flows and Zero Pressure-Gradient Turbulent Boundary Layers (Royal Institute of Technology, Stockholm, Sweden, 2009). (Ph.D. Thesis)
R. Örlü, A. Segalini, J. Klewicki, P.H. Alfredsson, High-order generalisation of the diagnostic scaling for turbulent boundary layers. J. Turbulence 17, 664–677 (2016)
M. Placidi, B. Ganapathisubramani, Turbulent flow over large roughness elements: Effect of frontal and plan solidity on turbulence statistics and structure. Boundary-Layer Meteorol. 167, 99–121 (2018)
M. Samie, I. Marusic, N. Hutchins, M.K. Fu, Y. Fan, M. Hultmark, A.J. Smits, Fully resolved measurements of turbulent boundary layer flows up to \(Re_\tau = 20,\!000\). J. Fluid Mech. 851, 391–415 (2018)
C. Sanmiguel Vila, R. Vinuesa, S. Discetti, A. Ianiro, P. Schlatter, R. Örlü, On the identification of well-behaved turbulent boundary layers. J. Fluid Mech. 822, 109138 (2017)
P. Schlatter, R. Örlü, Q. Li, G. Brethouwer, J.H.M. Fransson, A.V. Johansson, P.H. Alfredsson, D.S. Henningson, Turbulent boundary layers up to \(Re_\theta =2500\) studied through simulation and experiment. Phys. Fluids 21, 051702 (2009)
P. Schlatter, R. Örlü, Assessment of direct numerical simulation data of turbulent boundary layers. J. Fluid Mech 659, 116–126 (2010)
S.J. Zimmerman, S.K. Romero, J. Philip, J.C. Klewicki, Downstream evolution of junction flow three-component velocity fluctuations through the lens of the diagnostic plot. Int. J. Heat Fluid Flow 85, 108665 (2020)
Acknowledgements
We like to acknowledge professor Masaharu Matsubara for making the data from his laboratory available for Fig. 1. We also want to acknowledge the cooperation with professors Ian Castro and Joe Klewicki during the development of extensions of the diagnostic method, as well as many other researchers who have employed the idea and found it useful in various flow situations.
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Alfredsson, P.H., Segalini, A., Örlü, R. (2021). The Diagnostic Plot—A Tutorial with a Ten Year Perspective. In: Örlü, R., Talamelli, A., Peinke, J., Oberlack, M. (eds) Progress in Turbulence IX. iTi 2021. Springer Proceedings in Physics, vol 267. Springer, Cham. https://doi.org/10.1007/978-3-030-80716-0_17
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