Extracting discrete hierarchies of Townsend's wall-attached eddies

We decompose Townsend's wall-attached eddies from a multi-scale wall-bounded turbulent flow, extract discrete hierarchies of eddies, and study their geometrical characteristics. It is well known that the wall-attached eddies are hierarchical in nature and geometrically self-similar, but very few studies have successfully extracted them from a flow, especially from a decomposed flow. We propose a novel extraction scheme that is based on a spectral linear stochastic estimation methodology and the hierarchical nature of wall-attached eddies. The geometrical characteristics of the intense velocity clusters induced by attached eddies are studied via a clustering method. The extracted clusters are found to be self-similar in geometry that is consistent with Townsend's attached eddy hypothesis. A -2 power law of the population density of attached eddies is reported for the first time from data extraction.