On similitude of near wall turbulence in viscous sublayer

Power spectral density (PSD) of wall velocity gradient fluctuations has been measured using electrochemical (electrodiffusion) method in two rectangular channels with different hydraulic diameters and aspect ratio. The problem of the probes inertia at high frequency range has been smoothed by means of the transfer function; the reliability of the obtained results is justified by using of two circular probes with different diameter. For studied range of Reynolds numbers (6 × 10³ < Re _h < 4 × 10⁴) all spectra functions tend to a unique curve when a suitable dimensionless coordinates are used. These coordinates depend on the mean value of the velocity gradient S, the intensity of the velocity gradient fluctuations [`(s￠² )]overline {s'^2 } and the liquid viscosity ν, only. Thus, the obtained results reveal the similitude of the turbulence in the viscous sublayer with respect to Re number and flow geometry. Sure, this hypothesis should be tested with more representative base of experimental data. The revealed similitude can be important for chemical engineering applications. Indeed, for these applications the Reynolds numbers are rather small and correspond to the studied range and the intensity of the velocity gradient fluctuations are well related with the mean value of the velocity gradient value. So, the knowing of the mean velocity gradient S allows the prediction of the PSD of the velocity gradient fluctuations, if the viscosity of the fluid ν is known.