Comment on “Evolution of wall shear stress with Reynolds number in fully developed turbulent channel flow experiments”

The recent study by Gubian et al. [Phys. Rev. Fluids 4, 074606 (2019)], based on a new wall-shear-stress sensor in a low-Reynolds-number Re turbulent channel flow, came to the surprising conclusion that the magnitude of the fluctuating wall-shear stress ${\tau }_{w,rms}^{+}$ reaches an asymptotic value of 0.44 beyond the friction Reynolds number ${\text{Re}}_{\tau }\approx 600$. This statement is at odds with results from well-established direct numerical simulation (DNS) results that exceed the authors' highest Reynolds number by up to a factor of 5 while exhibiting a clear Reynolds-number dependence. Furthermore, they claim that “prior estimates of these quantities did not resolve the full range of wall-shear-stress fluctuations, which extended beyond 10 standard deviations above the mean.” This contradicts high-quality DNS results and calls for a more in-depth explanation, which is given in the present Comment. We shows that the measurements by Gubian et al. suffer from spatial-resolution issues among others, which when accounted for invalidate the statements made of an asymptotic state at ${\text{Re}}_{\tau }\approx 600$ and resurrects the Reynolds-number dependence of ${\tau }_{w,rms}^{+}$ for which DNS evidence exists exceeding ${\text{Re}}_{\tau }\approx 600$ by an order of magnitude.

Figure 1

Peak value of the rms value of the inner-scaled streamwise velocity fluctuations as a function of friction Reynolds number for fixed $L/\delta$ values from 0 to 0.07 (in the direction of the arrow), based on Eq. (3) in Ref. [35], where the red solid line corresponds to $L/\delta =1.25/30$ and the shaded area indicates the friction Reynolds-number range of the experiments of Gubian et al. [30], i.e., ${\text{Re}}_{\tau }=230–950$.

Figure 2

Reproduction of the data from Ref. [30] ($\circ$) including its $L^{+}$ corrected value ($▵$) based on Ref. [34]. Additionally, results from channel flow DNS are shown: +, [39, 40]; $*$, [28, 41]; $\times$, [42, 43]; $\square$, [27]; and $\diamond$, [17]. The dashed line indicates the correlation for zero-pressure-gradient turbulent boundary layers [44], while the shaded area indicates the friction Reynolds-number range based on which Gubian et al. [30] concluded that ${\tau }_{w,rms}^{+}$ reached its asymptotic value.