Reduced-order representation of superstructures in a turbulent boundary layer

The present work is devoted to a low-dimensional characterization of superstructures (SS) in a turbulent boundary layer (TBL). The main purpose is to provide new insight on the spatial correlation between SS and large-scale motion (LSM) with the help of reduced-order analysis via proper orthogonal decomposition (POD). A dataset of three-dimensional streamwise fluctuating velocity fields of a TBL with R e t = 1817, obtained by direct numerical simulation, is decomposed by POD into cross-sectional POD eigenmodes and streamwise-varying mode coefficients. The spatial pattern of the POD eigenmodes of leading-order POD modes, their characteristic length scales, as well as their geometric similarity are analyzed in detail. A conditional-average method is further proposed to yield a reduced-order representation of typical local geometric patterns of the SS, which are mainly contributed to by one particular observation mode. It is found that large-scale motion-like structures constitute the core region of SS. These conditional-averaged structures are treated as elementary cells, which jointly form the skeleton of SS, i.e., u SK which is low dimensionally reconstructed by the first six POD modes. It is found that u SK presents quasi-Gaussian behavior, suggesting a quasi-equilibrium state of elementary SS cells. Finally, ? u SK 2 ? ( y ) presents a log-law scaling with the decaying slope of A 1 SK = 1.49, but the log-law region is apparently higher than that of the original velocity field, i.e., ? u 2 ? ( y ).