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An idealised assessment of Townsend’s outer-layer similarity hypothesis for wall turbulence

Published online by Cambridge University Press:  24 February 2014

D. Chung ,
J. P. Monty  and
A. Ooi
D. Chung*
Affiliation:
Department of Mechanical Engineering, The University of Melbourne, Victoria 3010, Australia
J. P. Monty
Affiliation:
Department of Mechanical Engineering, The University of Melbourne, Victoria 3010, Australia
A. Ooi
Affiliation:
Department of Mechanical Engineering, The University of Melbourne, Victoria 3010, Australia
*
†Email address for correspondence: [email protected]
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Abstract

Direct numerical simulations of turbulent channel flow at the matched friction Reynolds number of 590, comparing the effect of no-slip versus shear-stress boundary conditions, reveal that the outer flow of wall turbulence, in accord with Townsend’s outer-layer similarity hypothesis, remains largely independent of the viscous sublayer. First- and second-order statistics, including spectra, agree closely from the buffer region out to the centre of the channel. Higher-order statistics also appear to obey the hypothesised similarity, although the influence of boundary conditions is more pronounced than in the lower-order statistics. The statistical agreement in the outer layer, in spite of the structural differences in the viscous sublayer, support Townsend’s idea that the primary effect of the wall is not the no-slip condition, but the impermeability condition imposed by a solid wall.

JFM classification

Turbulent Flows: Turbulent boundary layers Boundary Layers: Boundary layer structure Turbulent Flows: Turbulence simulation
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 742 , 10 March 2014 , R3
Copyright
© 2014 Cambridge University Press 

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References

Amir, M. & Castro, I. P. 2011 Turbulence in rough-wall boundary layers: universality issues. Exp. Fluids 51, 313–326.Google Scholar
Busse, A. & Sandham, N. D. 2012 Parametric forcing approach to rough-wall turbulent channel flow. J. Fluid Mech. 712, 169–202.Google Scholar
Castro, I. P., Cheng, H. & Reynolds, R. 2006 Turbulence over urban-type roughness: deductions from wind-tunnel measurements. Boundary-Layer Meteorol. 118, 109–131.CrossRefGoogle Scholar
Flack, K. A., Schultz, M. P. & Connelly, J. S. 2007 Examination of a critical roughness height for outer layer similarity. Phys. Fluids 19, 095104.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.CrossRefGoogle Scholar
Flores, O. & Jiménez, J. 2006 Effect of wall-boundary disturbances on turbulent channel flows. J. Fluid Mech. 566, 357–376.Google Scholar
Ganapathisubramani, B., Hutchins, N., Monty, J. P., Chung, D. & Marusic, I. 2012 Amplitude and frequency modulation in wall turbulence. J. Fluid Mech. 712, 61–91.Google Scholar
Guala, M., Hommema, S. E. & Adrian, R. J. 2006 Large-scale and very-large-scale motions in turbulent pipe flow. J. Fluid Mech. 554, 521–542.Google Scholar
Hutchins, N. & Marusic, I. 2007 Large-scale influences in near-wall turbulence. Phil. Trans. R. Soc. A 365, 647–664.Google Scholar
Kim, H. T., Kline, S. J. & Reynolds, W. C. 1971 The production of turbulence near a smooth wall in a turbulent boundary layer. J. Fluid Mech. 50, 133–160.Google Scholar
Kim, J. & Moin, P. 1985 Application of a fractional-step method to incompressible Navier–Stokes equations. J. Comput. Phys. 59, 308–323.Google Scholar
Kim, K. C. & Adrian, R. J. 1999 Very large-scale motion in the outer layer. Phys. Fluids 11, 417–422.Google Scholar
Klewicki, J., Fife, P. & Wei, T. 2009 On the logarithmic mean profile. J. Fluid Mech. 638, 73–93.Google Scholar
Krogstad, P.-Å. & Antonia, R. A. 1999 Surface roughness effects in turbulent boundary layers. Exp. Fluids 27, 450–460.CrossRefGoogle Scholar
Mathis, R., Hutchins, N. & Marusic, I. 2009 Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers. J. Fluid Mech. 628, 311–337.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
Mizuno, Y. & Jiménez, J. 2013 Wall turbulence without walls. J. Fluid Mech. 723, 429–455.Google Scholar
Monty, J. P., Stewart, J. A., Williams, R. C. & Chong, M. S. 2007 Large-scale features in turbulent pipe and channel flows. J. Fluid Mech. 589, 147–156.Google Scholar
Morinishi, Y., Lund, T. S., Vasilyev, O. V. & Moin, P. 1998 Fully conservative higher order finite difference schemes for incompressible flow. J. Comput. Phys. 143, 90–124.Google Scholar
Moser, R. D., Kim, J. & Mansour, N. N. 1999 Direct numerical simulation of turbulent channel flow up to $\textit {Re}_\tau = 590$ . Phys. Fluids 11, 943–945.Google Scholar
Nickels, T. B., Marusic, I., Hafez, S., Hutchins, N. & Chong, M. S. 2007 Some predictions of the attached eddy model for a high Reynolds number boundary layer. Phil. Trans. R. Soc. A 365, 807–822.Google Scholar
Orlandi, P., Leonardi, S., Tuzi, R. & Antonia, R. A. 2003 Direct numerical simulation of turbulent channel flow with wall velocity disturbnces. Phys. Fluids 15, 3587–3601.Google Scholar
Perry, A. E. & Chong, M. S. 1982 On the mechanism of wall turbulence. J. Fluid Mech. 119, 173–217.CrossRefGoogle Scholar
Schlatter, P. & Örlü, R. 2010 Quantifying the interaction between large and small scales in wall-bounded turbulent flows: a note of caution. Phys. Fluids 22, 051704.Google Scholar
Schoppa, W. & Hussain, F. 2002 Coherent structure generation in near-wall turbulence. J. Fluid Mech. 453, 57–108.Google Scholar
Schultz, M. P. & Flack, K. A. 2007 The rough-wall turbulent boundary layer from the hydraulically smooth to the fully rough regime. J. Fluid Mech. 580, 381–405.CrossRefGoogle Scholar
Spalart, P. R., Moser, R. D. & Rogers, M. M. 1991 Spectral methods for the Navier–Stokes equations with one infinite and two periodic directions. J. Comput. Phys. 96, 297–324.Google Scholar
Townsend, A. A. 1956 The Structure of Turbulent Shear Flow, 1st edn. Cambridge University Press.Google Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.Google Scholar