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A description of turbulent wall-flow vorticity consistent with mean dynamics

Published online by Cambridge University Press:  20 November 2013

J. C. Klewicki
J. C. Klewicki*
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Melbourne, VIC 3010, Australia Department of Mechanical Engineering, University of New Hampshire, Durham, NH 03824, USA
*
†Email address for correspondence: [email protected]
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Abstract

A depiction of the mean and fluctuating vorticity structure in turbulent wall flows is presented and described within the context of the self-similar properties admitted by the mean dynamical equation. Data from a relatively wide range of numerical and physical experiments are used to explore and clarify the structure postulated. The mean vorticity indicator for the onset of the four-layer regime of the mean dynamics is revealed. With increasing Reynolds number, the mean vorticity is shown to segregate into two increasingly well-defined domains. Half of the mean vorticity concentrates into a near-wall region of width (relative to the overall flow width) that diminishes proportionally to the inverse square root of Reynolds number. The remainder of the mean vorticity is spread, with diminishing amplitude, over an outer domain that approaches the overall flow width at high Reynolds number. Vorticity stretching and reorientation are surmised to be the characteristic mechanisms accounting for the inner domain behaviour of both the mean and fluctuating vorticity. Vorticity dispersion via advective transport is surmised to be the characteristic mechanism in the outer domain. In this domain, the fluctuating enstrophy approaches that of the instantaneous enstrophy with increasing Reynolds number. This underpins an emerging self-similarity between the mean and r.m.s. vorticity in the domain where the mean velocity profile is logarithmic. The Reynolds number dependence of a number of properties associated with the vorticity field is explored and quantified. The study closes with brief account of the combined vortical and mean dynamical structure of turbulent wall flows.

JFM classification

Turbulent Flows: Turbulence theory Turbulent Flows: Turbulent Flows Turbulent Flows: Turbulent boundary layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 737 , 25 December 2013 , pp. 176 - 204
Copyright
©2013 Cambridge University Press 

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References

Abe, H, Kawamura, H. & Matsuo, Y. 2004 Surface heat-flux fluctuations in a turbulent channel flow up to $R{e}_{\tau } = 1020$ with $Pr= 0. 025$ and 0.71. Intl J. Heat Fluid Flow 25, 404–419.Google Scholar
Adrian, R. J., Meinhart, C. D. & Tomkins, C. D. 2000 Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422, 1–54.Google Scholar
Cheng, C. 2011 Numerical study of internal wall-bounded turbulent flows. PhD thesis, University of Melbourne, Victoria, Australia.Google Scholar
Coles, D. E. 1956 The law of the wake in turbulent boundary layers. J. Fluid Mech. 1, 191–226.Google Scholar
Dimotakis, P. E. 2000 The mixing transition in turbulent flows. J. Fluid Mech. 409, 69–98.Google Scholar
Elsnab, J., Klewicki, J., Maynes, D. & Ameel, T. 2011 Mean dynamics of transitional channel flow. J. Fluid Mech. 678, 451–481.Google Scholar
Eyink, G. 2008 Turbulent flow in pipes and channels as cross-stream ‘inverse cascades’ of vorticity. Phys. Fluids 20, 125101.Google Scholar
Fife, P., Klewicki, J., McMurtry, P. & Wei, T. 2005a Stress gradient balance layers and scale hierarchies in wall-bounded turbulence. J. Fluid Mech. 532, 165–189.Google Scholar
Fife, P., Klewicki, J., McMurtry, P. & Wei, T. 2005b Multiscaling in the presence of indeterminacy: wall-induced turbulence. Multiscale Model. Simul. 4, 936–959.Google Scholar
Fife, P., Klewicki, T. & Wei, 2009 Time averaging in turbulence settings may reveal an infinite hierarchy of length scales. J. Discrete Continuous Dyn. Syst. 24, 781–807.Google Scholar
Hoyas, S. & Jimenez, J. 2006 Scaling the velocity fluctuations in turbulent channels up to $R{e}_{\tau } = 2003$ . Phys. Fluids 18, 011702.Google Scholar
Hunt, J. C. R., Eames, I., Da Silva, C. B & Westerweel, J. 2011 Interfaces and inhomogeneous turbulence. Phil. Trans. R. Soc. Lond. A 369, 811–832.Google Scholar
Hunt, J. C. R., Eames, I., Westerweel, J., Davidson, P. A., Voropayev, S., Fernando, J. & Braza, M. 2010 Thin shear layers – the key to turbulence structure? J. Hydro-environmental Res. 4, 75–82.Google Scholar
Hutchins, N., Nickles, T. B., Marusic, I. & Chong, M. S. 2009 Hot-wire spatial resolution issues in wall-bounded turbulence. J. Fluid Mech. 635, 103–136.CrossRefGoogle Scholar
Ishihara, T., Hunt, J. C. R. & Kaneda, Y. 2011 Conditional analysis near strong shear layers in DNS of isotropic turbulence at high Reynolds number. J. Phys.: Conf. Ser. 318, 042004.Google Scholar
von Kármán, T. 1930 Mechanische Ahnlichkeit und Turbulenz. Nachr. Ges. Wiss. Göttingen, Math-Phys. Klasse 155–162.Google Scholar
Klewicki, J. 2010 Reynolds number dependence, scaling, and dynamics of turbulent boundary layers. Trans. ASME: J. Fluids Engng 132, 094001.Google Scholar
Klewicki, J. C. 2013a Self-similar mean dynamics in turbulent wall-flows. J. Fluid Mech. 718, 596–621.Google Scholar
Klewicki, J. C. 2013b On the singular nature of turbulent boundary layers. Proc. IUTAM, Procedia IUTAM 9, 69–78.Google Scholar
Klewicki, J., Chin, C., Blackburn, H., Ooi, A. & Marusic, I. 2012 Emergence of the four layer dynamical regime in turbulent pipe flow. Phys. Fluids 24, 045107.Google Scholar
Klewicki, J., Ebner, R. & Wu, X. 2011 Mean dynamics of transitional boundary-layer flow. J. Fluid Mech. 682, 617–651.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, 119–142.Google Scholar
Klewicki, J. C. & Falco, R. E. 1996 Spanwise vorticity structure in turbulent boundary layers. Intl J. Heat Fluid Flow 17, 363–376.Google Scholar
Klewicki, J., Fife, P. & Wei, T. 2009 On the logarithmic mean profile. J. Fluid Mech. 638, 73–93.Google Scholar
Klewicki, J., Fife, P., Wei, T. & McMurtry, P. 2007 A physical model of the turbulent boundary layer consonant with mean momentum balance structure. Phil. Trans. R. Soc. Lond. A 365, 823–839.Google Scholar
Klewicki, J. C., Murray, J. A. & Falco, R. E. 1994 Vortical motion contributions to stress transport in turbulent boundary layers. Phys. Fluids 6, 277–286.CrossRefGoogle Scholar
Klewicki, J. C., Priyadarshana, P. J. A. & Metzger, M. M. 2008 Statistical structure of the fluctuating wall pressure and its in-plane gradients at high Reynolds number. J. Fluid Mech. 609, 195–220.Google Scholar
Laadhari, F. 2002 On the evolution of maximum turbulent kinetic energy production in a channel flow. Phys. Fluids 14, L65–L68.Google Scholar
Lighthill, M. J. 1963 Boundary layer theory. In Laminar Boundary Layers (ed. Rosenhead, L.), Oxford University Press.Google Scholar
Lighthill, M. J. 1958 On displacement thickness. J. Fluid Mech. 4, 383–392.Google Scholar
Marusic, I. & Adrian, R. J. 2013 The eddies and scales of wall turbulence. In Ten Chapters in Turbulence (ed. Davidson, P., Kaneda, Y. & Sreenivasan, K. R.), Cambridge University Press.Google Scholar
Marusic, I., Monty, J., Hultmark, M. & Smits, A. 2013 On the logarithmic region in wall turbulence. J. Fluid Mech. 716, R3.Google Scholar
McKeon, B. J. 2003 High Reynolds number turbulent pipe flow. PhD thesis, Princeton University, Princeton, New Jersey.Google Scholar
McKeon, B. J. & Morrison, J. F. 2007 Asymptotic scaling in turbulent pipe flow. Phil. Trans. R. Soc. Lond. A 365, 771–787.Google Scholar
Meinhart, C. & Adrian, R. J. 1995 On the existence of uniform momentum zones in a turbulent boundary layers. Phys. Fluids 7, 694–696.Google Scholar
Mellor, G. L. 1972 The large Reynolds number asymptotic theory of turbulent boundary layers. Intl J. Engng Sci. 10, 851–873.Google Scholar
Metzger, M. 2006 Length and time scales of the near-surface axial velocity in a high Reynolds number turbulent boundary layer. Intl J. Heat Fluid Flow 27, 534–541.Google Scholar
Metzger, M. M. & Klewicki, 2001 A comparative study of near-wall turbulence in high and low Reynolds number boundary layers. Phys. Fluids 13, 692–701.Google Scholar
Monty, J. P. 2005 Developments in smooth wall turbulent duct flow. PhD thesis, University of Melbourne, Victoria, Australia.Google Scholar
Morrill-Winter, C. & Klewicki, J. 2013 Influences of boundary layer scale separation on the vorticity transport contribution to turbulent inertia. Phys. Fluids 25, 015108.CrossRefGoogle Scholar
Morris, S. C., Stolpa, S. R., Slaboch, P. E. & Klewicki, J. C. 2007 Near-surface particle image velocimetry measurements in a transitionally rough-wall atmospheric boundary layer. J. Fluid Mech. 580, 319–338.Google Scholar
Nagib, H., Chauhan, K. & Monkewitz, P. 2007 Approach to an asymptotic state for zero pressure gradient turbulent boundary layers. Phil. Trans. R. Soc. Lond. A 365, 755–770.Google Scholar
Oweis, G. F., Winkel, E. S., Cutbrith, J. M., Ceccio, S. L., Perlin, M. & Dowling, D. R. 2010 The mean velocity profile of a smooth-flat-plate turbulent boundary layer at high Reynolds number. J. Fluid Mech. 665, 357–381.Google Scholar
Perry, A. & Chong, M. 1982 On the mechanism of wall turbulence. J. Fluid Mech. 119, 173–217.Google Scholar
Perry, A., Henbest, S. & Chong, M. 1986 A theoretical and experimental study of wall-turbulence. J. Fluid Mech. 165, 163–199.Google Scholar
Perry, A. & Marusic, I. 1995 A wall-wake model for the turbulence structure of boundary layers. Part 1. Extension of the attached eddy hypothesis. J. Fluid Mech. 298, 361–388.Google Scholar
Priyadarshana, P. J. A. & Klewicki, J. C. 2003 Reynolds number scaling of wall layer velocity-vorticity products. In Reynolds Number Scaling in Turbulent Flow (ed. Smits, A.J.), pp. 117–123. Kluwer Academic Publishers.Google Scholar
Priyadarshana, P. J. A. & Klewicki, J. C. 2004 Study of the motions contributing to the Reynolds stress in high and low Reynolds number turbulent boundary layers. Phys. Fluids 16, 4586–4600.Google 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, 307–346.Google Scholar
Sayadi, T., Hamman, C. W. & Moin, P. 2013 Direct numerical simulation of complete H-type and K-type transitions with implications for the dynamics of turbulent boundary layers. J. Fluid Mech. 724, 480–509.Google Scholar
Schlatter, P. & Orlu, R. 2010 Assessment of direct numerical simulation data of turbulent boundary layers. J. Fluid Mech. 659, 116–126.Google Scholar
Stanislas, M., Perret, L. & Foucaut, J. M. 2008 Vortical structures in the turbulent boundary layer: a possible route to a universal representation. J. Fluid Mech. 602, 327–382.Google Scholar
Tennekes, H. & Lumley, J. 1972 A First Course in Turbulence. MIT.CrossRefGoogle Scholar
Townsend, A. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.Google 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, 303–327.Google Scholar
Wosnik, M., Castillo, L. & George, W. K. 2000 A theory for turbulent pipe and channel flows. J. Fluid Mech. 421, 115–145.Google Scholar
Wu, X. & Moin, P. 2008 A direct numerical simulation study on the mean velocity characteristics in turbulent pipe flow. J. Fluid Mech. 608, 81–112.Google Scholar
Wu, X. & Moin, P. 2009 Direct numerical simulation of turbulence in a nominally zero-pressure-gradient flat-plate boundary layer. J. Fluid Mech. 630, 5–41.Google Scholar
Yajnik, K. S. 1970 Asymptotic theory of turbulent shear flows. J. Fluid Mech. 42, 411–427.Google Scholar
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