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Statistical structure of turbulent-boundary-layer velocity–vorticity products at high and low Reynolds numbers
- P. J. A. Priyadarshana, J. C. Klewicki, S. Treat, J. F. Foss
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- Journal:
- Journal of Fluid Mechanics / Volume 570 / 10 January 2007
- Published online by Cambridge University Press:
- 14 October 2021, pp. 307-346
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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.
Statistical structure of the fluctuating wall pressure and its in-plane gradients at high Reynolds number
- J. C. KLEWICKI, P. J. A. PRIYADARSHANA, M. M. METZGER
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- Journal:
- Journal of Fluid Mechanics / Volume 609 / 25 August 2008
- Published online by Cambridge University Press:
- 31 July 2008, pp. 195-220
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The fluctuating wall pressure and its gradients in the plane of the surface were measured beneath the turbulent boundary layer that forms over the salt playa of Utah's west desert. Measurements were acquired under the condition of near-neutral thermal stability to best mimic the canonical zero-pressure-gradient boundary-layer flow. The Reynolds number (based on surface-layer thickness, δ, and the friction velocity, uτ) was estimated to be 1 × 106 ± 2 × 105. The equivalent sandgrain surface roughness was estimated to be in the range 15≤ks+≤85. Pressure measurements acquired simultaneously from an array of up to ten microphones were analysed. A compact array of four microphones was used to estimate the instantaneous streamwise and spanwise gradients of the surface pressure. Owing to the large length scales and low flow speeds, attaining accurate pressure statistics in the present flow required sensors capable of measuring unusually low frequencies. The effects of imperfect spatial and temporal resolution on the present measurements were also explored. Relative to pressure, pressure gradients exhibit an enhanced sensitivity to spatial resolution. Their accurate measurement does not, however, require fully capturing the low frequencies that are inherent and significant in the pressure itself. The present pressure spectra convincingly exhibit over three decades of approximately −1 slope. Comparisons with low-Reynolds-number data support previous predictions that the inner normalized wall pressure variance increases logarithmically with Reynolds number. The wall pressure autocorrelation exhibits its first zero-crossing at an advected length that is between one tenth and one fifth of the surface-layer thickness. Under any of the normalizations investigated, the present surface vorticity flux intensity values are difficult to reconcile with low-Reynolds-number data trends. Inner variables, however, do yield normalized flux intensity values that are of the same order of magnitude at low and high Reynolds number. Spectra reveal that even at high Reynolds number, the primary contributions to the pressure gradient intensities occur over a relatively narrow frequency range. This frequency range is shown to be consistent with the scale of the sublayer pocket motions. In accord with low-Reynolds-number data, the streamwise pressure gradient signals at high Reynolds number are also characterized by statistically significant pairings of opposing sign fluctuations.