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Law of the wall for small-scale streamwise turbulence intensity in high-Reynolds-number turbulent boundary layers

B. Ganapathisubramani*

  • University of Southampton, Southampton SO17 1BJ, United Kingdom

  • *g.bharath@soton.ac.uk
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Phys. Rev. Fluids 3, 104607 – Published 31 October, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.104607

Abstract

Following the dimensional analysis approach carried out in previous studies, it is hypothesized that the small-scale fluctuations should only depend on the inner scales, analogous to the Prandtl's law of the wall for the mean flow. This allows us to examine the high-frequency regime of the streamwise energy spectra where a “law of the wall” in spectra would hold. Observations in high-Reynolds-number turbulent boundary layer data indicate that a conservative estimate for the start of this law of the wall is f+=0.005 (which corresponds to 200 viscous time units) across a range of wall-normal positions and Reynolds numbers. This is sufficient to capture the energetic viscous-scaled motions such as the near-wall streaks, which have a timescale of approximately 100 viscous units. This spectral collapse is consistent with the observations in internal flows and external flows in other studies. Furthermore, the spectral collapse leads to a universal scaling (based on skin-friction velocity and kinematic viscosity) for the small-scale streamwise turbulence variance (consistent with the hypothesis) across the entire boundary layer. A logarithmic variation of this small-scale variance is observed farther away from the wall.

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Phys. Rev. Fluids 3, 104607– Published 31 October, 2018
  • Received 22 May 2018
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