A new formulation for the streamwise turbulence intensity distribution in wall-bounded turbulent flows

Abstract

The distribution of the streamwise velocity turbulence intensity has recently been discussed in several papers both from the viewpoint of new experimental results as well as attempts to model its behavior. In the present paper numerical and experimental data from zero pressure-gradient turbulent boundary layers, channel and pipe flows over smooth walls have been analyzed by means of the so called diagnostic plot introduced by Alfredsson & Örlü [P.H. Alfredsson, R. Örlü, The diagnostic plot–a litmus test for wall bounded turbulence data, Eur. J. Mech. B Fluids 29 (2010) 403–406]. In the diagnostic plot the local turbulence intensity is plotted as function of the local mean velocity normalized with a reference velocity scale. Alfredsson et al. [P.H. Alfredsson, A. Segalini, R. Örlü, A new scaling for the streamwise turbulence intensity in wall-bounded turbulent flows and what it tells us about the outer peak, Phys. Fluids 23 (2011) 041702] observed that in the outer region of the boundary layer a universal linear decay of the turbulence intensity independent of the Reynolds number exists. This approach has been generalized for channel and pipe flows as well, and it has been found that the deviation from the previously established linear region appears at a given wall distance in viscous units (around 120) for all three canonical flows. Based on these results, new empirical fits for the streamwise velocity turbulence intensity distribution of each canonical flow are proposed. Coupled with a mean streamwise velocity profile description the model provides a composite profile for the streamwise variance profile that agrees nicely with existing numerical and experimental data. Extrapolation of the proposed scaling to high Reynolds numbers predicts the emergence of a second peak of the streamwise variance profile that at even higher Reynolds numbers overtakes the inner one.