Evidence that superstructures comprise of self-similar coherent motions in high $Re_{\tau}$ boundary layers

Abstract

We present experimental evidence that the superstructures in turbulent boundary layers comprise of smaller, geometrically self-similar coherent motions. The evidence comes from identifying and analyzing instantaneous superstructures from large-scale particle image velocimetry datasets acquired at high Reynolds numbers, capable of capturing streamwise elongated motions extending up to 12 times the boundary layer thickness. Given the challenge in identifying the constituent motions of the superstructures based on streamwise velocity signatures, a new approach is adopted that analyzes the wall-normal velocity fluctuations within these very long motions, which reveals the constituent motions unambiguously. The conditional streamwise energy spectra of the wall-normal fluctuations, corresponding exclusively to the superstructure region, are found to exhibit the well-known distance-from-the-wall scaling in the intermediate scale range. Similar characteristics are also exhibited by the Reynolds shear stress co-spectra estimated for the superstructure region, suggesting that geometrically self-similar motions are the constituent motions of these very-large-scale structures. Investigation of the spatial organization of the wall-normal momentum-carrying eddies also lends empirical support to the concatenation hypothesis for the formation of the superstructures. Association between the superstructures and self-similar motions is reaffirmed on comparing the vertical correlations of the momentum carrying motions, which are found to match with the mean correlations. The mean vertical coherence of these motions, investigated for the log-region across three decades of Reynolds numbers, exhibits a unique distance-from-the-wall scaling invariant with Reynolds number. The findings support the prospect for modelling these dynamically significant motions via data-driven coherent structure-based models.Comment: Manuscript accepted for the Journal of Fluid Mechanics, with 25 pages, 15 figure