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Statistical structure of turbulent-boundary-layer velocity–vorticity products at high and low Reynolds numbers

Published online by Cambridge University Press:  14 October 2021

P. J. A. Priyadarshana ,
J. C. Klewicki ,
S. Treat  and
J. F. Foss
P. J. A. Priyadarshana
Affiliation:
Department of Mechanical Engineering, University of Utah, Salt Lake City, UT 84112, USA
J. C. Klewicki
Affiliation:
Department of Mechanical Engineering, University of Utah, Salt Lake City, UT 84112, USA
S. Treat
Affiliation:
Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824, USA
J. F. Foss
Affiliation:
Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824, USA
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Abstract

The mean wall-normal gradients of the Reynolds shear stress and the turbulent kinetic energy have direct connections to the transport mechanisms of turbulent-boundary-layer flow. According to the Stokes–Helmholtz decomposition, these gradients can be expressed in terms of velocity–vorticity products. Physical experiments were conducted to explore the statistical properties of some of the relevant velocity–vorticity products. The high-Reynolds-number data (Rθ ≃ O(106), where θ is the momentum thickness) were acquired in the near neutrally stable atmospheric-surface-layer flow over a salt playa under both smooth- and rough-wall conditions. The low-Rθ data were from a database acquired in a large-scale laboratory facility at 1000 > Rθ > 5000. Corresponding to a companion study of the Reynolds stresses (Priyadarshana & Klewicki, Phys. Fluids, vol. 16, 2004, p. 4586), comparisons of low- and high-Rθ as well as smooth- and rough-wall boundary-layer results were made at the approximate wall-normal locations yp/2 and 2yp, where yp is the wall-normal location of the peak of the Reynolds shear stress, at each Reynolds number. In this paper, the properties of the vωz, wωy and uωz products are analysed through their statistics and cospectra over a three-decade variation in Reynolds number. Here u, v and w are the fluctuating streamwise, wall-normal and spanwise velocity components and ωy and ωz are the fluctuating wall-normal and spanwise vorticity components. It is observed that v–ωz statistics and spectral behaviours exhibit considerable sensitivity to Reynolds number as well as to wall roughness. More broadly, the correlations between the v and ω fields are seen to arise from a ‘scale selection’ near the peak in the associated vorticity spectra and, in some cases, near the peak in the associated velocity spectra as well.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 570 , 10 January 2007 , pp. 307 - 346
Copyright
Copyright © Cambridge University Press 2007

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Footnotes

†

Present address: Department of Mechanical and Nuclear Engineering, Kansas State University, Manhattan, KS 66506, USA.

‡

Present address: Department of Mechanical Engineering, University of New Hampshire, Durham, NH 03824, USA.

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