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

Abstract

\"Orl\"u and Schlatter [R. \"Orl\"u and P. Schlatter, preceding Comment, Phys. Rev. Fluids 5, 127601 (2020)] claim that the evolution of the turbulent intensity of the wall-shear stress (${\ensuremath{\tau}}_{{w}_{RMS}}/\ensuremath{\langle}{\ensuremath{\tau}}_{w}\ensuremath{\rangle}$) to a constant value at sufficiently large Reynolds number in our previous work [P.-A. Gubian et al., Phys. Rev. Fluids 4, 074606 (2019)] is the result of ``strong effects of insufficient spatial resolution'' of the sensor used therein, which, when corrected for, restores a continual Reynolds number dependence of ${\ensuremath{\tau}}_{{w}_{RMS}}/\ensuremath{\langle}{\ensuremath{\tau}}_{w}\ensuremath{\rangle}$. They also argue that the temporal resolution of the sensor used in our work had not been characterized. Herein, it is demonstrated that there are multiple other studies that have shown (by way of direct numerical simulation) that ${\ensuremath{\tau}}_{{w}_{RMS}}/\ensuremath{\langle}{\ensuremath{\tau}}_{w}\ensuremath{\rangle}$ becomes constant and independent of Reynolds number. Moreover, as \"Orl\"u and Schlatter themselves note, their proposed correction substantially overcorrects the data, such that the corrected data are ``too high and strong,'' which is presumably because they are applying a correction designed for velocity measurements to a sensor that (directly) measures wall-shear stress and is governed by different physical principles. Finally, the frequency response of the sensor used in our previous work (a flush-mounted hot-wire sensor in which the hot-wire is installed over a small rectangular cavity in the base of the sensor) has indeed been characterized and documented, by Sturzebecher et al. [D. Sturzebecher et al., Exp. Fluids 31, 294 (2001)]. Therein, the sensor was shown to have a cutoff frequency that exceeds 30 kHz, whereas the highest frequencies of the flow in our previous work did not exceed 10 kHz.