The Use of Pattern Recognition and Proper Orthogonal Decomposition in Identifying the Structure of Fully-Developed Free Turbulence

Abstract

The eigenvectors obtained from proper orthogonal decomposition (POD) are used as the selection criteria to classify the individual events contained in date files of two-component velocity signals recorded in the non-homogeneous (vertical) and homogeneous (horizontal) planes of a fully-developed turbulent cylinder wake. This procedure uses the dominant eigenvectors from POD as initial templates to perform a pattern recognition (PR) analysis of the signals so that the individual coherent events appearing randomly in the signals can be educed more objectively. It is found that the prototype or ensemble average of the group of events classified as the large-scale structure in the vertical plane has a circulatory motion with strong negative streamwise and outward lateral velocity fluctuations. In the horizontal plane, the average structure is a double roller with negative streamwise velocity fluctuations in its centerplane. The class of instantaneous events selected contribute significantly to the variance in the outer intermittent region, but much less in the fully turbulent core. While the first eigenvector from POD captures some of the features shown by this prototype, it is not enough to depict by itself all the characteristics shown by the ensemble average of the repetitive three-dimensional instantaneous events that occur in the fully-developed turbulent wake.