Length-Scale Similarity of Turbulent Organized Structures over Surfaces with Different Roughness Types

Abstract

We examine the similarity of turbulent organized structures over smooth and very rough wall flows. Turbulent flow fields in horizontal cross-sections were measured using particle image velocimetry, and the characteristics of turbulent organized structures over four types of surfaces were investigated. Measurements were conducted at several measurement heights across the internal boundary layer. The length and width of turbulence structures were quantified using a two-point correlation method. We selected two thresholds of two-point correlation coefficients to consider both large-scale and small-scale structures; the validity of these choices was examined through the analyses using proper orthogonal decomposition. For large-scale structures, the length and aspect ratios (streamwise length/spanwise width) of structures were highly correlated with the velocity gradient for each measurement height and boundary-layer thickness. This relationship was also examined in the results of previous studies, and the scaling of the aspect ratio with the non-dimensional velocity gradient again showed the importance of the velocity gradient, with slight differences found between smooth and rough surfaces. In contrast, the small-scale structures exhibited weak dependency on the velocity gradient and boundary-layer thickness. Instantaneous snapshots of turbulent organized structures at the same shear level also displayed differences in small-scale structures, but the structures of the organized motions resembled each other, as in the results of the two-point correlation method.