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

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 has a time scale 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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ORCID for Bharathram Ganapathisubramani: orcid.org/0000-0001-9817-0486

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