Single-point structure tensors in turbulent channel flows with smooth and wavy walls

Abstract

A long-standing problem in turbulence modeling is that the Reynolds stress tensor alone is not necessarily sufficient to characterize the transient and nonequilibrium behaviors of turbulence under arbitrary mean deformation or frame rotation. A more complete single-point characterization of the flow can be obtained using the structure dimensionality, circulicity, and inhomogeneity tensors. These tensors are one-point correlations of local stream vector gradients and carry nonlocal information regarding the structure of the flow field. We explore the potential of these tensors to improve understanding of complex turbulent flows using direct numerical simulation of flows in channels with a smooth wall and a two-dimensional sinusoidal wavy wall. To enforce no-slip and no-penetration conditions at wavy-wall boundaries, an immersed boundary method for the stream vector Poisson equation was adopted within the framework of Stylianou, Pecnik, and Kassinos, “A general framework for computing the turbulence structure tensors,” Comput. Fluids 106, 54–66 (2015). The results show that the effects of wall waviness on the inclination and aspect ratio of the two-point velocity correlation near the wall are reproduced qualitatively by their corresponding single-point tensor representations. In the outer layer, good quantitative agreement is achieved for both parameters. Additional observations on the structural changes of turbulence due to wall waviness and their relevance to turbulence modeling with surface roughness are discussed. The findings of this investigation suggest that single-point structure tensors can be appended to the modeling basis for inhomogeneous flows with geometrically complex boundaries, such as rough-wall flows, to develop improved turbulence models.