Single-point structure tensors in wall turbulence

A long-standing problem in turbulence modeling is that the Reynolds stress tensor alone is not necessarily sufficient to characterize the transient and non-equilibrium behaviors of turbulence under arbitrary mean deformation or frame rotation. More complete flow characterizations include additional single-point structure tensors (e.g. Kassinos, Reynolds and Rogers, JFM 2001), such as the dimensionality, circulicity and inhomogeneity tensors. These tensors are one-point correlations of local streamfunction vector and can carry non-local information on turbulence structure. A seminal question involves the information supplied by these tensors and the potential utility of this additional information to improve the predictive fidelity of a model. In this talk, we explore the role of these tensors in smooth- and rough-wall channel flows using existing DNS data. Roughness effects on the inclination and aspect ratio of two-point velocity correlations inside the roughness sublayer are qualitatively reproduced by their corresponding single-point tensor representations; in the outer layer, such representations are almost exact. Other observations on turbulence-structure changes on account of wall roughness and their relevance to turbulence modeling will be discussed.