Skip to main content Accessibility help
×
Home

Mean dynamics of transitional boundary-layer flow

  • J. KLEWICKI (a1) (a2), R. EBNER (a1) and X. WU (a3)

Abstract

The dynamical mechanisms underlying the redistribution of mean momentum and vorticity are explored for transitional two-dimensional boundary-layer flow at nominally zero pressure gradient. The analyses primarily employ the direct numerical simulation database of Wu & Moin (J. Fluid Mech., vol. 630, 2009, p. 5), but are supplemented with verifications utilizing subsequent similar simulations. The transitional regime is taken to include both an instability stage, which effectively generates a finite Reynolds stress profile, −ρuv(y), and a nonlinear development stage, which progresses until the terms in the mean momentum equation attain the magnitude ordering of the four-layer structure revealed by Wei et al. (J. Fluid Mech., vol. 522, 2005, p. 303). Self-consistently applied criteria reveal that the third layer of this structure forms first, followed by layers IV and then II and I. For the present flows, the four-layer structure is estimated to be first realized at a momentum thickness Reynolds number Rθ = U θ/ν ≃ 780. The first-principles-based theory of Fife et al. (J. Disc. Cont. Dyn. Syst. A, vol. 24, 2009, p. 781) is used to describe the mean dynamics in the laminar, transitional and four-layer regimes. As in channel flow, the transitional regime is marked by a non-negligible influence of all three terms in the mean momentum equation at essentially all positions in the boundary layer. During the transitional regime, the action of the Reynolds stress gradient rearranges the mean viscous force and mean advection profiles. This culminates with the segregation of forces characteristic of the four-layer regime. Empirical and theoretical evidence suggests that the formation of the four-layer structure also underlies the emergence of the mean dynamical properties characteristic of the high-Reynolds-number flow. These pertain to why and where the mean velocity profile increasingly exhibits logarithmic behaviour, and how and why the Reynolds stress distribution develops such that the inner normalized position of its peak value, ym+, exhibits a Reynolds number dependence according to .

Copyright

Corresponding author

Email address for correspondence: joe.klewicki@unh.edu

References

Hide All
Adrian, R. 2007 Hairpin vortex organization in wall turbulence. Phys. Fluids 19, 041301.
Afzal, N. 1982 Fully developed turbulent flow in a pipe: an intermediate layer. Ing.-Arch. 52, 355377.
Antonia, R., Teitel, M., Kim, J. & Browne, L. 1992 Low-Reynolds-number effects in a fully developed turbulent channel flow. J. Fluid Mech. 236, 579605.
Bailey, S., Hultmark, M., Smits, A. & Schultz, M. 2008 Azimuthal structure of turbulence in high Reynolds number pipe flow. J. Fluid Mech. 615, 121138.
Balakumar, B. & Adrian, R. 2007 Large- and very-large-scale motions in channel and boundary-layer flows. Phil. Trans. R. Soc. Lond. A 365, 665681.
Buschmann, M., Indinger, T. & Gad-el-Hak, M. 2009 Near-wall behavior of turbulent wall-bounded flows. Intl J. Heat Fluid Flow 30, 9931006.
Ching, C. Y., Djendi, L. & Antonia, R. A. 1995 Low Reynolds-number effects in a turbulent boundary layer. Exp. Fluids 19, 6168.
Criminale, W., Jackson, T. & Joslin, R. 2003 Theory and Computation in Hydrodynamic Stability. Cambridge University Press.
Dean, R. 1978 Reynolds number dependence of skin friction and other bulk flow variables in two-dimensional rectangular duct flow. J. Fluids Engng 100, 215223.
DeGraaff, D. B. & Eaton, J. K. 2000 Reynolds-number scaling of the flat-plate turbulent boundary layer. J. Fluid Mech. 422, 319346.
Elsnab, J., Klewicki, J., Maynes, D. & Ameel, T. 2011 Mean dynamics of transitional channel flow. J. Fluid Mech. 678, 451481.
Elsnab, J., Maynes, D., Klewicki, J. & Ameel, T. 2010 Mean flow structure in high aspect ratio microchannel flows. Exp. Therm. Fluid Sci. 34, 10771088.
Eyink, G. 2008 Turbulent flow in pipes and channels as cross-stream ‘inverse cascades’ of vorticity. Phys. Fluids 20, 125101.
Fife, P., Klewicki, J., McMurtry, P. & Wei, T. 2005 a Multiscaling in the presence of indeterminacy: wall-induced turbulence. Multiscale Model. Simul. 4, 936959.
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.
Fife, P., Wei, T., Klewicki, J. & McMurtry, P. 2005 b Stress gradient balance layers and scale hierarchies in wall bounded turbulent flows. J. Fluid Mech. 532, 165189.
Ganapathisubramani, B. 2008 Statistical structure of momentum sources and sinks in the outer region of a turbulent boundary layer. J. Fluid Mech. 606, 225237.
Guala, M., Hommema, S. & Adrian, R. 2006 Large-scale and very-large-scale motions in turbulent pipe flow. J. Fluid Mech. 554, 521542.
Hoyas, S. & Jimenez, J. 2006 Scaling the velocity fluctuations in turbulent channels up to Re τ = 2003. Phys. Fluids 18, 011702.
Jordinson, R. 1970 The flat plate boundary layer. Part 1. Numerical integration of the Orr–Sommerfeld equation. J. Fluid Mech. 43, 801811.
Klewicki, J. 2010 Reynolds number dependence, scaling, and dynamics of turbulent boundary layers. J. Fluids Engng 132, 094001.
Klewicki, J., Fife, P. & Wei, T. 2009 On the logarithmic mean profile. J. Fluid Mech. 638, 7393.
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, 823839.
Kuroda, A., Kasagi, N. & Hirata, M. 1989 A direct numerical simulation of the fully developed turbulent channel flow. In Proc. Intl Symp. on Computational Fluid Dynamics, Nagoya, Japan, pp. 11741179.
Laadhari, F. 2002 On the evolution of maximum turbulent kinetic energy production in a channel flow. Phys. Fluids 14, L65L68.
Long, R. & Chen, T.-C. 1981 Experimental evidence for the existence of the mesolayer in turbulent systems. J. Fluid Mech. 105, 1959.
Marusic, I. 2009 Unraveling turbulence near walls. J. Fluid Mech. 630, 14.
Metzger, M., Adams, P. & Fife, P. 2008 Mean momentum balance in moderately favourable pressure gradient turbulent boundary layers. J. Fluid Mech. 617, 107140.
Monkewitz, P., Chauhan, K. & Nagib, H. 2008 Comparison of mean flow similarity laws in zero-pressure-gradient turbulent boundary layers. Phys. Fluids 20, 105102.
Monty, J., Stewart, J., Williams, R. & Chong, M. 1981 Large scale features in turbulent pipe and channel flows. J. Fluid Mech. 589, 147156.
Nagib, H. & Chauhan, K. 2008 Variation of von Kármán coefficient in canonical flows. Phys. Fluids 20, 101518.
Nagib, H., Chauhan, K. & Mokewitz, P. 2007 Approach to an asymptotic state for zero pressure gradient turbulent boundary layers. Phil. Trans. R. Soc. Lond. A 365, 755770.
Osterlund, J., Johansson, A., Nagib, H. & Hites, M. 2000 A note on the overlap region in turbulent boundary layers. Phys. Fluids 12, 14.
Perry, A. & Chong, M. 1982 On the mechanism of wall turbulence. J. Fluid Mech. 119, 173217.
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, 361388.
Schlatter, P. & Orlu, R. 2010 Assessment of direct numerical simulation data of turbulent boundary layers. J. Fluid Mech. 659, 116126.
Schlichting, H. & Gersten, K. 2000 Boundary Layer Theory. Springer.
Schoppa, W. & Hussain, F. 2002 Coherent structure generation in near-wall turbulence. J. Fluid Mech. 453, 57108.
Sherman, F. 1990 Viscous Flows. McGraw-Hill.
Smits, A., McKeon, B. & Marusic, I. 2011 High Reynolds number wall turbulence. Annu. Rev. Fluid Mech. 43, 253375.
Sreenivasan, K. 1989 The turbulent boundary layer. In Frontiers in Experimental Fluid Mechanics (ed. Gad-el-Hak, M.), pp. 159209. Springer.
Sreenivasan, K. & Bershadskii, A. 2006 Finite-Reynolds-number effects in turbulence using logarithmic expansions. J. Fluid Mech. 554, 477498.
Sreenivasan, K. & Sahay, A. 1997 The persistence of viscous effects in the overlap region and the mean velocity in turbulent pipe and channel flows. In Self-Sustaining Mechanisms of Wall Turbulence (ed. Panton, R.), pp. 253272. Computational Mechanics Publications.
Tomkins, C. & Adrian, R. 2003 Spanwise structure and scale growth in turbulent boundary layers. J. Fluid Mech. 490, 3774.
Townsend, A. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.
Waleffe, F. 1997 On a self-sustaining process in shear flows. Phys. Fluids 7, 883900.
Wei, T., Fife, P. & Klewicki, J. 2007 On scaling the mean momentum balance and its solutions in turbulent Couette–Poiseuille flow. J. Fluid Mech. 573, 371398.
Wei, T., Fife, P., Klewicki, J. & McMurtry, P. 2005 a Properties of the mean momentum balance in turbulent boundary layer, pipe and channel flows. J. Fluid Mech. 522, 303327.
Wei, T., McMurtry, P., Klewicki, J. & Fife, P. 2005 b Mesoscaling of the Reynolds shear stress in turbulent channel and pipe flows. AIAA J. 43, 23502353.
Wu, X. 2010 Establishing the generality of three phenomena using a boundary layer with free-stream passing wakes. J. Fluid Mech. 664, 193219.
Wu, X. & Moin, P. 2009 Direct numerical simulation of turbulence in a nominally zero-pressure-gradient flat-plate boundary layer. J. Fluid Mech. 630, 541.
Wu, X. & Moin, P. 2010 Transitional and turbulent boundary layer with heat transfer. Phys. Fluids 22, 085105.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Related content

Powered by UNSILO

Mean dynamics of transitional boundary-layer flow

  • J. KLEWICKI (a1) (a2), R. EBNER (a1) and X. WU (a3)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.