Similarity of apparently random structures in the outer region of wall turbulence

Abstract

Structural similarities between samples of individual, apparently random structures in various wall-bounded turbulent flows are examined using a template-matching technique. Two-dimensional structural patterns obtained by particle image velocimetry in a turbulent boundary layer are sampled along streamwise lines to extract one-dimensional spatial series that are used as templates. These templates are correlated with time series data obtained in turbulent pipe flow, turbulent channel flow, and atmospheric boundary layer flow in order to determine the frequency and coherency with which similar structures occur. The results indicate that a small ensemble of templates from one flow can be concatenated to represent a large fraction of the entire velocity–time history of each of the other flows by using episodes during which the various templates correlate well. Thus, within the pipe flow, channel flow, and atmospheric boundary layer, one frequently finds detailed time series segments that coincide closely, i.e., in fine detail, with a handful of templates found in a laboratory boundary layer. This type of similarity, which includes seemingly random, fine details at large and small scales, is much stronger than similarity based on statistical comparisons. The individual templates that work best, i.e., those that most frequently yield episodes of high correlation, are segments of hairpin-vortex packets. The high frequency with which these particular structures occur suggests that they are common features of all wall-bounded turbulent flows, including turbulent flows at very high Reynolds number such as the atmospheric boundary layer.