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Self-preservation in a zero pressure gradient rough-wall turbulent boundary layer

Published online by Cambridge University Press:  22 December 2015

K. M. Talluru ,
L. Djenidi ,
Md. Kamruzzaman  and
R. A. Antonia
K. M. Talluru*
Affiliation:
Discipline of Mechanical Engineering, School of Engineering, University of Newcastle, Newcastle, 2308 NSW, Australia
L. Djenidi
Affiliation:
Discipline of Mechanical Engineering, School of Engineering, University of Newcastle, Newcastle, 2308 NSW, Australia
Md. Kamruzzaman
Affiliation:
Discipline of Mechanical Engineering, School of Engineering, University of Newcastle, Newcastle, 2308 NSW, Australia
R. A. Antonia
Affiliation:
Discipline of Mechanical Engineering, School of Engineering, University of Newcastle, Newcastle, 2308 NSW, Australia
*
†Email address for correspondence: [email protected]
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Abstract

A self-preservation (SP) analysis is carried out for a zero pressure gradient (ZPG) rough-wall turbulent boundary layer with a view to establishing the requirements of complete SP (i.e. SP across the entire layer) and determining if these are achievable. The analysis shows that SP is achievable in certain rough-wall boundary layers (irrespectively of the Reynolds number $Re$), when the mean viscous stress is zero or negligible compared to the form drag across the entire boundary layer. In this case, the velocity scale $u^{\ast }$ must be constant, the length scale $l$ should vary linearly with the streamwise distance $x$ and the roughness height $k$ must be proportional to $l$. Although this result is consistent with that of Rotta (Prog. Aeronaut. Sci., vol. 2 (1), 1962, pp. 1–95), it is derived in a more rigorous manner than the method employed by Rotta. Further, it is noted that complete SP is not possible in a smooth-wall ZPG turbulent boundary layer. The SP conditions are tested against published experimental data on both a smooth wall (Kulandaivelu, 2012, PhD thesis, The University of Melbourne) and a rough wall, where the roughness height increases linearly with $x$ (Kameda et al., J. Fluid Sci. Technol., vol. 3 (1), 2008, pp. 31–42). Complete SP in a ZPG rough-wall turbulent boundary layer seems indeed possible when $k\propto x$.

JFM classification

Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 788 , 10 February 2016 , pp. 57 - 69
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Copyright
© 2016 Cambridge University Press 

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