Reynolds Number Invariance of the Structure Inclination Angle in Wall Turbulence

Abstract

Cross correlations of the fluctuating wall-shear stress and the streamwise velocity in the logarithmic region of turbulent boundary layers are reported over 3 orders of magnitude change in Reynolds number. These results are obtained using hot-film and hot-wire anemometry in a wind tunnel facility, and sonic anemometers and a purpose-built wall-shear stress sensor in the near-neutral atmospheric surface layer on the salt flats of Utah's western desert. The direct measurement of fluctuating wall-shear stress in the atmospheric surface layer has not been available before. Structure inclination angles are inferred from the cross correlation results and are found to be invariant over the large range of Reynolds number. The findings justify the prior use of low Reynolds number experiments for obtaining structure angles for near-wall models in the large-eddy simulation of atmospheric surface layer flows.

On the Formation Mechanisms of Artificially Generated High Reynolds Number Turbulent Boundary Layers

“…11b for the correlations presented above show 14 • ≤ α ≤ 18 • without any clear trend depending on the trip used. This result is in a good agreement with previous studies such α = 18 • by Brown and Thomas (1977), α = 16 • by Robinson (1986), α = 15 • by Boppe et al (1999) or α = 14 • by Marusic and Heuer (2007). Note that, for brevity, results are only shown for the highest Re, i.e.…”

Interactions within the turbulent boundary layer at high Reynolds number

“…• angles reported in the literature and confirm the findings of Marusic & Heuer (2007) that the angle of inclination in the surface layer is substantially invariant, in good agreement with lower-Reynolds-number results, and very sensitive to the reference location. A local maximum of the cross-correlation in the region of this angle can be distinguished up to z + ∼ 4 × 10 4 .…”

“…Figures 7 and 9 support the Reynolds number invariance of the structural angle observed by Marusic & Heuer (2007) and identify coherence with a signature reminiscent of the ramp-like structures associated with hairpin packets at a lower Reynolds number. In addition, in the same region of the order of thousands of viscous wall units, similar results in terms of the temporal phase relationship between the small and large scales are observed here and in the lower-Reynolds-number studies of Bandyopadhyay & Hussain (1984) (figure 17).…”

“…Figure 9 shows the cross-correlations and the resultant variation of α with wall-normal distance. An accurate estimate of this angle requires a velocity signal very close to the wall or a direct measure of the shear stress (see Marusic & Heuer 2007); however, our closest measurement to the wall is at z + ∼ 10 and corresponds to a non-negligible mean velocity. A better estimate of the angle, denoted by α 0 , can be obtained by assuming zero mean velocity at the wall, i.e.…”

Wall shear stress fluctuations: Mixed scaling and their effects on velocity fluctuations in a turbulent boundary layer

“…This cross-correlation has a well-defined peak which is located at an increasing time-lag τ for increasing values of y. Figure 11(b) and previous author's data [29,31] suggest that the time lag of the correlation maximum, τ peak , scales as y/ū(y).…”