Reduced-order representation of superstructures in a turbulent boundary layer

Abstract

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 Reτ=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., uSK which is low dimensionally reconstructed by the first six POD modes. It is found that uSK presents quasi-Gaussian behavior, suggesting a quasi-equilibrium state of elementary SS cells. Finally, ⟨uSK2⟩(y) presents a log-law scaling with the decaying slope of A1SK=1.49, but the log-law region is apparently higher than that of the original velocity field, i.e., ⟨u2⟩(y).