Meandering features of wall-attached structures in turbulent boundary layer

Abstract

In wall turbulence, meandering behaviors of large-scale structures observed in the logarithmic layer are a crucial spatial feature to understand the spatial organization of these structures and to improve the structure-based turbulence model. These structures extend from the near-wall region to the edge of boundary layers (8). Thus, their meandering motions leave an imprint on the two-point turbulence statistics across the flow, espe-cially in the logarithmic region. Herein, we demonstrate the influence of the meandering motions of wall-attached structures on the two-point correlation and the premultiplied two-dimensional spectra by analyzing the direct numerical simulation data of the turbulent boundary layer at Re tau approximate to 1000. The meandering magnitudes of wall-attached structures increase with their height (ly) but significantly differ among the identified structures even at a given ly. In addition, the wall-attached structures of streamwise velocity fluctuations (u) are found to be aligned along with a preferred spanwise offset regardless of the meandering motion. This feature is confirmed through the conditional two-point correlations of u within the meandering structures, which leads to a distinct X pattern in the logarithmic region. We further examine the spectral behavior of the meandering structures across the streamwise and spanwise wavelengths (lambda x and lambda z, respectively) through the premultiplied two-dimensional spectra. With increasing meandering magnitudes, the energy spectra are more inclined to the lambda z direction. Furthermore, the energy spectra of the strong meandering structures are bounded by a linear relationship lambda x similar to lambda z over the large-scale range, rem-iniscent of self-similar scaling predicted by the attached-eddy hypothesis. In particular, the upper bound is aligned along lambda x approximate to 2 lambda z over lambda z > 8, which is absent in the energy spectral of the total u. This result reveals that the meandering motions allow the large-scale structures to contain wide spanwise scale energy that is self-similar in the logarithmic region. Finally, a discussion on the near-wall parts of the meandering structures is given with an emphasis on Townsend's inactive eddies.