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Effect of the intermittency dynamics on single and multipoint statistics of turbulent boundary layers

Published online by Cambridge University Press:  10 June 2020

Nico Reuther Open the ORCID record for Nico Reuther [Opens in a new window]  and
Christian J. Kähler
Nico Reuther*
Affiliation:
Institute of Fluid Mechanics and Aerodynamics, Universität der Bunderwehr München, 85577Neubiberg, Germany
Christian J. Kähler
Affiliation:
Institute of Fluid Mechanics and Aerodynamics, Universität der Bunderwehr München, 85577Neubiberg, Germany
*
†Email address for correspondence: nico.reuther@unibw.de
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Abstract

The instantaneous velocity field of turbulent flows is traditionally described in a statistical sense as a sum of an ensemble or temporal mean velocity at a specific location and a fluctuating term. While the Reynolds decomposition is well-established for fully turbulent flows, its applicability for flows that show intermittent behaviour is questionable. As intermittency is an integral part of turbulent boundary layer and turbulent jet and wake flows, an analysis of the effect of the intermittency on the statistical quantities is of fundamental interest. In this work, the effect of intermittency on single and multipoint statistics is studied for an experimentally obtained turbulent boundary layer data set at high Reynolds numbers by means of three different decomposition approaches. The analysis clearly shows that the Reynolds decomposition is only valid for single point statistics in the inner fully turbulent region of wall-bounded flows. In the wake region of a turbulent boundary layer, the Reynolds decomposition overestimates the turbulent kinetic energy due to the intermittency of the turbulent/non-turbulent interface. It is shown herein that these artefacts can be reduced or even completely avoided by applying either the boundary layer height or zonal based decomposition approach. In this study, the limitations of the different methods are analysed in detail and the approaches are evaluated comparatively by investigating statistical quantities such as turbulence intensity, anisotropy of fluctuations and characteristic length scales of coherent motions. The results make it possible to better understand and interpret the characteristics of the turbulent statistics of intermittent flows.

JFM classification

Turbulent Flows: Turbulent boundary layers Turbulent Flows: Intermittency
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 897 , 25 August 2020 , A11
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

Adrian, R. J., Christensen, K. T. & Liu, Z.-C. 2000 Analysis and interpretation of instantaneous turbulent velocity fields. Exp. Fluids 29, 275–290.CrossRefGoogle Scholar
Anand, R. K., Boersma, B. J. & Agrawal, A. 2009 Detection of turbulent/non-turbulent interface for an axisymmetric turbulent jet: evaluation of known criteria and proposal of a new criterion. Exp. Fluids 47, 995–1007.CrossRefGoogle Scholar
Antonia, R. A. 1972 Conditionally sampled measurement near the outer edge of a turbulent boundary layer. J. Fluid Mech. 56, 1–18.CrossRefGoogle Scholar
Bross, M., Fuchs, T. & Kähler, C. J. 2019 Interaction of coherent flow structures in adverse pressure gradient turbulent boundary layers. J. Fluid Mech. 873, 287–321.CrossRefGoogle Scholar
Chauhan, K., Philip, J., de Silva, C. M., Hutchins, N. & Marusic, I. 2014 The turbulent/non-turbulent interface and entrainment in a boundary layer. J. Fluid Mech. 742, 119–151.CrossRefGoogle Scholar
Coles, D. 1956 The law of the wake in the turbulent boundary layer. J. Fluid Mech. 1, 119–151.CrossRefGoogle Scholar
Corrsin, S.1943 Investigation of flow in an axially symmetrical heated jet of air. NACA Tech. Rep. WR W-94.Google Scholar
Falco, R. E. 1977 Coherent motion in the outer region of turbulent boundary layers. Phys. Fluids 20, 124–132.CrossRefGoogle Scholar
Ganapathisumbramani, B., Hutchins, N., Hambleton, W. T., Longmire, E. K. & Marusic, I. 2005 Investigation of large-scale coherence in a turbulent boundary layer using two-point correlations. J. Fluid Mech. 524, 57–80.CrossRefGoogle Scholar
Hedley, T. B. & Keffer, J. F. 1974 Some turbulent/non-turbulent properties of the outer intermittent region of a boundary layer. J. Fluid Mech. 64, 645–678.CrossRefGoogle Scholar
Herget, W. 1985 Der Zoo der Mittelwerte. Mathematik Lehren 8, 50–51.Google Scholar
Holzner, M., Liberzon, A., Guala, M., Tsinober, A. & Kinzelbach, W. 2006 Generalized detection of a turbulent front generated by an oscillating grid. Exp. Fluids 41, 711–719.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007 Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 1–28.CrossRefGoogle Scholar
Jiménez, J., Hoyas, S., Simens, M. P. & Mizuno, Y. 2010 Turbulent boundary layer and channels at moderate Reynolds numbers. J. Fluid Mech. 657, 335–360.CrossRefGoogle Scholar
Kähler, C. J.2004 The significance of coherent flow structures for the turbulent mixing in wall-bounded flows. PhD thesis, DLR Forschungsbericht 2004–24.Google Scholar
Kähler, C. J., Sammler, B. & Kompenhans, J. 2002 Generation and control of tracer particles for optical flow investigations in air. Exp. Fluids 33, 736–742.CrossRefGoogle Scholar
Kähler, C. J., Scharnowski, S. & Cierpka, C. 2012a On the resolution limit of digital particle image velocimetry. Exp. Fluids 52, 1629–1639.CrossRefGoogle Scholar
Kähler, C. J., Scharnowski, S. & Cierpka, C. 2012b On the uncertainty of digital PIV and PTV near walls. Exp. Fluids 52, 1641–1656.CrossRefGoogle Scholar
Kähler, C. J., Scholz, U. & Ortmanns, J. 2006 Wall-shear-stress and near-wall turbulence measurements up to single pixel resolution by means of long-distance micro-PIV. Exp. Fluids 41, 327–341.CrossRefGoogle Scholar
Klebanoff, P. S.1955 Characteristics of turbulence in a boundary layer with zero pressure gradient. NACA-TR-1247, pp. 1135–1153.Google Scholar
Knopp, T., Novara, M., Schanz, D., Schülein, E., Schröder, A., Reuther, N. & Kähler, C. J. 2018 A New Experiment of a Turbulent Boundary Layer Flow at Adverse Pressure Gradient for Validation and Improvement of RANS Turbulence Models. pp. 85–94. Springer.Google Scholar
Kovasznay, L. S. G., Kibens, V. & Blackwelder, R. F. 1970 Large-scale motion in the intermittent region of a turbulent boundary layer. J. Fluid Mech. 41, 283–325.CrossRefGoogle Scholar
Kwon, Y. S., Hutchins, N. & Monty, J. P. 2016 On the use of the Reynolds decomposition in the intermittent region of turbulent boundary layers. J. Fluid Mech. 794, 5–16.CrossRefGoogle Scholar
Lee, J. H. & Sung, H. J. 2011 Very-large-scale motions in a turbulent boundary layer. J. Fluid Mech. 673, 80–120.CrossRefGoogle Scholar
Millikan, C. 1938 A critical discussion of turbulent flows in channels and circular tubes. In Proceedings of the 5th International Congress on Applied Mechanics, Cambridge, pp. 386–392. John Wiley.Google Scholar
Novara, M., Schanz, D., Reuther, N., Kähler, C. J. & Schröder, A. 2016 Lagrangian 3D particle tracking in high-speed flows: Shake-The-Box for multi-pulse systems. Exp. Fluids 57, 128.CrossRefGoogle Scholar
Philip, J., de Silva, C. M. C. M. & Marusic, I. 2014 Multiscale analysis of fluxes at the turbulent/non-turbulent interface in high Reynolds number boundary layers. Phys. Fluids 26, 015105.CrossRefGoogle Scholar
Raffel, M., Willert, C. E., Scarano, F., Kähler, C. J., Werely, S. T. & Kompenhans, J. 2018 Particle Image Velocimetry – A Practical Guide. Springer.CrossRefGoogle Scholar
Rahgozar, S. & Maciel, Y. 2012 Statistical analysis of low- and high-speed large-scale structures in the outer region of an adverse pressure gradient turbulent boundary layer. J. Turbul. 13, 1–24.Google Scholar
Reuther, N. & Kähler, C. J. 2018 Evaluation of large-scale turbulent/non-turbulent interface detection methods for wall-bounded flows. Exp. Fluids 59, 121.CrossRefGoogle Scholar
Reynolds, O. 1895 On the dynamical theory of incompressible viscous fluids and the determination of the criterion. Phil. Trans. R. Soc. Lond. 186, 123–164.Google Scholar
Sillero, J. A., Jiménez, J. & Moser, R. D. 2013 One-point statistics for turbulent wall-bounded flows at Reynolds numbers up to 𝛿+ ≈ 2000. Phys. Fluids 25, 105102.CrossRefGoogle Scholar
Tomkins, C. D. & Adrian, R. J. 2003 Spanwise structure and scale growth in turbulent boundary layers. J. Fluid Mech. 490, 37–74.CrossRefGoogle Scholar
Townsend, A. A. 1948 Local isotropy in the turbulent wake of a cylinder. Austral. J. Sci. Res. 1, 161–174.Google Scholar
Wallace, J. M. 2013 Highlights from 50 years of turbulent boundary layer research. J. Turbul. 13 (53), 1–70.Google Scholar