Scaling of wall-parallel velocity variances in turbulent channel flow: An objectivity test

In this work, popular scaling laws for the streamwise and spanwise velocity variances in the inner and overlap regions of turbulent channel flow are evaluated using publicly available numerical datasets up to a friction Reynolds number R e τ ≈ 1 0 4 . The evaluation is done indirectly by leveraging a property of the kinematic Reynolds-stress tensor: its material-frame indifference. The stress is passed to a rotating frame where the components of interest are linear combinations of the original wall-parallel variances and where any applicable scaling to both variances is carried over to the new components. Analyses of two-term inner expansions obtained for the R e τ -dependent functions F = ln R e τ , 1 / ln R e τ , and R e τ − α for the inner region and F = ln R e τ and R e τ − α for the overlap reveal that F = R e τ − α provides the best overall fit to the data in the new frame. Here, the power-law coefficient α is taken equal to 1/4 (Chen and Sreenivasan, 2021), yet it is highlighted that other similar α values may yield as good results as α = 1 / 4 . • First application of the objectivity axiom for testing Reynolds-stress scaling in wall turbulence. • Scaling laws such as log-law and power-law trends are tested using available DNS channel flow datasets. • After a change of observer, a power-law approximation fits the data better both in the inner-layer and overlap regions.