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Shared dynamical features of smooth- and rough-wall boundary-layer turbulence

Published online by Cambridge University Press:  03 March 2016

R. L. Ebner
Affiliation:
The MITRE Corporation, Bedford, MA 01730, USA
Faraz Mehdi
Affiliation:
Light Industrial Systems, Hypertherm Inc, Lebanon, NH 03766, USA
J. C. Klewicki*
Affiliation:
Department of Mechanical Engineering, University of New Hampshire, Durham, NH 03824, USA Department of Mechanical Engineering, University of Melbourne, Victoria 3010, Australia
*
Email address for correspondence: joe.klewicki@unh.edu

Abstract

The structure of smooth- and rough-wall turbulent boundary layers is investigated using existing data and newly acquired measurements derived from a four element spanwise vorticity sensor. Scaling behaviours and structural features are interpreted using the mean momentum equation based framework described for smooth-wall flows by Klewicki (J. Fluid Mech., vol. 718, 2013, pp. 596–621), and its extension to rough-wall flows by Mehdi et al. (J. Fluid Mech., vol. 731, 2013, pp. 682–712). This framework holds potential relative to identifying and characterizing universal attributes shared by smooth- and rough-wall flows. As prescribed by the theory, the present analyses show that a number of statistical features evidence invariance when normalized using the characteristic length associated with the wall-normal transition to inertial leading-order mean dynamics. On the inertial domain, the spatial size of the advective transport contributions to the mean momentum balance attain approximate proportionality with this length over significant ranges of roughness and Reynolds number. The present results support the hypothesis of Mehdi et al., that outer-layer similarity is, in general, only approximately satisfied in rough-wall flows. This is because roughness almost invariably leaves some imprint on the vorticity field; stemming from the process by which roughness influences (generally augments) the near-wall three-dimensionalization of the vorticity field. The present results further indicate that the violation of outer similarity over regularly spaced spanwise oriented bar roughness correlates with the absence of scale separation between the motions associated with the wall-normal velocity and spanwise vorticity on the inertial domain.

Type
Papers
Copyright
© 2016 Cambridge University Press 

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Footnotes

The author’s affiliation with The MITRE Corporation is provided for identification purposes only, and is not intended to convey or imply MITRE’s concurrence with, or support for, the positions, opinions or viewpoints expressed by the author.

References

Alfredsson, P. H., Segalini, A. & Orlu, R. 2011 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.Google Scholar
Antonia, R., Zhu, Y. & Kim, J. 1993 On the measurement of lateral velocity derivatives in turbulent flows. Exp. Fluids 15, 6569.CrossRefGoogle Scholar
Brzek, B., Cal, R. B., Johansson, G. & Castillo, L. 2007 Inner and outer scalings in rough surface zero pressure gradient turbulent boundary layers. Phys. Fluids 19, 065101.Google Scholar
Castro, B., Segalini,  & Alfredsson, P. H. 2013 Outer layer turbulence intensities in smooth- and rough-wall boundary layers. J. Fluid Mech. 727, 119131.CrossRefGoogle Scholar
Chin, C., Philip, J., Klewicki, J., Ooi, A. & Marusic, I. 2014 Reynolds number dependent turbulent inertia and onset of log-region in pipe flows. J. Fluid Mech. 757, 747769.Google Scholar
Connelly, J. S., Schultz, M. P. & Flack, K. A. 2006 Velocity-defect scaling for turbulent boundary layers with a range of relative roughness. Exp. Fluids 40 (2), 188195.Google Scholar
Davidson, P. A. & Krogstad, P. A. 2014 A universal scaling for low-order structure functions in the log-law region of smooth- and rough-wall boundary layers. J. Fluid Mech. 752, 140156.CrossRefGoogle Scholar
DeGraaff, D. B. & Eaton, J. K. 2000 Reynolds number scaling of the flat-plate turbulent boundary layer. J. Fluid Mech. 422, 319346.CrossRefGoogle Scholar
Djenidi, l., Antonia, R. A., Amielh, M. & Anselmet, F. 2008 A turbulent boundary layer over a two-dimensional rough wall. Exp. Fluids 44, 3747.Google Scholar
Duvvuri, S. & McKeon, B. J. 2015 Triadic scale interactions in a turbulent boundary layer. J. Fluid Mech. 767, R4-1.Google Scholar
Ebner, R.2014 Influences of roughness on the inertial mechanism of turbulent boundary-layer scale separation. PhD Dissertation, University of New Hampshire, Durham, New Hampshire, USA.Google Scholar
Efros, V. & Krogstad, P-.Å. 2011 Development of a turbulent boundary layer after a step from smooth to rough surface. Exp. Fluids 51, 15631575.CrossRefGoogle Scholar
Fife, P., Klewicki, J., McMurtry, P. & Wei, T. 2005 Multiscaling in the presence of indeterminacy: wall-induced turbulence. Multiscale Model. Simul. 4, 936959.Google Scholar
Fife, P., Klewicki, J. & Wei, T. 2009 Time averaging in turbulence settings may reveal an infinite hierarchy of length scales. J. Discrete Continuous Dyn. Syst. 24, 781807.Google Scholar
Flack, K. A., Schultz, M. P. & Shapiro, T. A. 2005 Experimental support for Townsend’s Reynolds number similarity hypothesis on rough walls. Phys. Fluids 17, 035102.Google Scholar
Foss, J. F. & Haw, R. 1990 Transverse vorticity measurements using a compact array of four sensors. ASME FED 97, 7176.Google Scholar
Fukagata, K., Iwamotu, K. & Kasagi, N. 2002 Contributions of Reynolds stress distribution to the skin friction in wall-bounded flows. Phys. Fluids 14, L73L76.Google Scholar
Hansen, A. 1964 Similarity Analysis of Boundary Value Problems in Engineering. Prentice-Hall.Google Scholar
Hauptman, Z.2010 Characterization of a low-speed boundary layer wind tunnel. MS thesis, University of New Hampshire, Durham, New Hampshire, USA.Google Scholar
Hong, J., Katz, J. & Schultz, M. P. 2011 Near-wall turbulence statistics and flow structures over three-dimensional roughness in a turbulent channel flow. J. Fluid Mech. 667, 137.Google Scholar
Hoyas, S. & Jimenez, J. 2006 Scaling the velocity fluctuations in turbulent channels up to $Re_{{\it\tau}}=2003$ . Phys. Fluids 18, 011702.Google Scholar
Hutchins, N., Nickels, T. B., Marusic, I. & Chong, M. S. 2009 Hot-wire spatial resolution issues in wall-bounded turbulence. J. Fluid Mech. 635, 103136.Google Scholar
Jiménez, J. 2004 Turbulent flows over rough walls. Annu. Rev. Fluid Mech. 36, 173196.Google Scholar
Klewicki, J. C. & Falco, R. E. 1990 On accurately measuring statistics associated with small-scale structure in turbulent boundary layers using hot-wire probes. J. Fluid Mech. 219, 119142.Google Scholar
Klewicki, J. C., Gendrich, C. P., Foss, J. F. & Falco, R. E. 1990 On the sign of the instantaneous spanwise vorticity component in the near-wall region of turbulent boundary layers. Phys. Fluids A 2, 14971501.CrossRefGoogle Scholar
Klewicki, J. C. 1997 Self-sustaining traits of near-wall motions underlying boundary layer stress transport. In Self-Sustaining Mechanisms of Wall Turbulence (ed. Panton, R.), pp. 135166. Computational Mechanics Publications.Google Scholar
Klewicki, J. 2013a Self-similar mean dynamics in turbulent wall flows. J. Fluid Mech. 718, 596621.CrossRefGoogle Scholar
Klewicki, J. 2013b A description of turbulent wall-flow vorticity consistent with mean dynamics. J. Fluid Mech. 737, 176204.Google Scholar
Klewicki, J., Ebner, R. & Wu, X. 2011 Mean dynamics of transitional boundary layer flow. J. Fluid Mech. 682, 617651.Google Scholar
Klewicki, J., Morrill-Winter, C. & Zhou, A. 2015 Inertial logarithimic layer properties and self-similar mean dynamics. In Proceedings of Turbulent Shear Flow Phenomena 9; paper no. 188, University of Melbourne.Google Scholar
Krogstad, P-.Å. & Antonia, R. A. 1999 Surface roughness effects in turbulent boundary layers. Exp. Fluids 27 (5), 450460.Google Scholar
Lighthill, M. J. 1958 On displacement thickness. J. Fluid Mech. 4, 383392.CrossRefGoogle Scholar
Ligrani, P. & Moffat, R. 1986 Structure of transitionally rough and fully rough turbulent boundary layers. J. Fluid Mech. 162, 6998.Google Scholar
Marusic, I., Monty, J., Hultmark, M. & Smits, A. 2013 On the logarithmic region in wall turbulence. J. Fluid Mech. 716, R311.Google Scholar
Mathis, R., Marusic, I., Hutchins, N. & Sreenivasan, K. R. 2011 The relationship between the velocity skewness and the amplitude modulation of the small scale by the large scale in turbulent boundary layers. Phys. Fluids 23, 121702.Google Scholar
Meinhart, C. & Adrian, R. J. 1995 On the existence of uniform momentum zones in turbulent boundary layers. Phys. Fluids 7, 694696.Google Scholar
Mehdi, F.2012 Mean force structure and scaling of rough-wall turbulent bound ary layers. PhD Dissertation, University of New Hampshire, Durham, New Hampshire, USA.Google Scholar
Mehdi, F., Klewicki, J. & White, C. 2010 Mean momentum balance analysis of rough-wall turbulent boundary layers. Physica D 239, 13291337.CrossRefGoogle Scholar
Mehdi, F., Klewicki, J. & White, C. 2013 Mean force structure and its scaling in rough-wall turbulent boundary layers. J. Fluid Mech. 731, 682712.Google Scholar
Mehdi, F. & White, C. 2011 Integral form of the skin friction coefficient suitable for experimental data. Exp. Fluids. 50, 4351.Google Scholar
Meneveau, C. & Marusic, I. 2013 Generalized logarithmic law for high-order moments in turbulent boundary layers. J. Fluid Mech. 719, R111.CrossRefGoogle Scholar
Metzger, M. M. & Klewicki, J. C. 2001 A comparative study of near-wall turbulence in high and low Reynolds number boundary layers. Phys. Fluids 13, 692701.CrossRefGoogle Scholar
Meyers, T., Forest, J. B. & Devenport, W. J. 2015 The wall-pressure spectrum of high-Reynolds-number turbulent boundary-layer flows over rough surfaces. J. Fluid Mech. 768, 261293.Google Scholar
Monty, J. P., Allen, J. J., Lien, K. & Chong, M. S. 2011a Modification of the large-scale features of high Reynolds number wall turbulence by passive surface obtrusions. Exp. Fluids 51, 17551763.Google Scholar
Monty, J. P., Klewicki, J. C. & Ganapathisubramani, B. 2011b Characteristics of momentum sources and sinks in turbulent channel flow. In Proceedings of Turbulent Shear Flow Phenomena 7; paper no. IC4P, University of Ottawa.Google Scholar
Morrill-Winter, C. & Klewicki, J. 2013 Influences of boundary layer scale separation on the vorticity transport contribution to turbulent inertia. Phys. Fluids 24, 015108.Google Scholar
Murlis, J., Tsai, H. M. & Bradshaw, P. 1982 The structure of turbulent boundary layers at low Reynolds numbers. J. Fluid Mech. 122, 1356.CrossRefGoogle Scholar
Priyadarshana, P. J. A., Klewicki, J. C., Treat, S. & Foss, J. F. 2007 Statistical structure of turbulent-boundary layer velocity-vorticity products at high and low Reynolds numbers. J. Fluid Mech. 570, 307346.Google Scholar
Rajagopalan, S. & Antonia, R. A. 1993 Structure of the velocity field associated with the spanwise vorticity in the wall region of a turbulent boundary layer. Phys. Fluids A 5, 25022510.Google Scholar
Raupach, M. R., Antonia, R. A. & Rajagopalan, S. 1991 Rough-wall boundary layers. Appl. Mech. Rev. 44, 125.Google Scholar
Saha, S., Klewicki, J., Ooi, A. & Blackburn, H. 2015 On scaling pipe flows with sinusoidal transversely-corrugated walls: analysis of data from the laminar to low Reynolds number turbulent regime. J. Fluid Mech. 779, 245274.Google Scholar
Schlatter, P. & Orlu, R. 2010 Assessment of direct numerical simulation data of turbulent boundary layers. J. Fluid Mech. 659, 116126.Google Scholar
Schultz, M. P. & Flack, K. A. 2007 The rough-wall turbulent boundary layers from the hydraulically smooth to the fully rough regime. J. Fluid Mech. 580, 381405.Google Scholar
Sreenivasan, K. R. 1987 A unified view of the origin and morphology of the turbulent boundary layer structure. In Turbulence Management and Relaminarization (ed. Liepmann, H. W. & Narasimha, R.), pp. 3760. Springer.Google Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.Google Scholar
Townsend, A. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.Google Scholar
Tropea, C., Yarin, A. & Foss, J. F.(Eds) 2007 Handbook of Experimental Fluid Mechanics. Springer.Google Scholar
Vincenti, P., Klewicki, J., Morrill-Winter, C., White, C. & Wosnik, M. 2013 Streamwise velocity statistics in turbulent boundary layers that spatially develop to high Reynolds number. Exp. Fluids 54, 16291638.Google Scholar
Volino, R. J., Schultz, M. P. & Flack, K. A. 2011 Turbulence structure in boundary layers over periodic two- and three-dimensional roughness. J. Fluid Mech. 676, 172190.CrossRefGoogle Scholar
Wei, T., Fife, P., Klewicki, J. & McMurtry, P. 2005 Properties of the mean momentum balance in turbulent boundary layer, pipe and channel flows. J. Fluid Mech. 522, 303327.Google Scholar
Zhou, A. & Klewicki, J. 2015 Properties of the streamwise velocity fluctuations in the inertial layer of turbulent boundary layers and their connection to self-similar mean dynamics. Intl J. Heat Fluid Flow 51, 372382.Google Scholar