Observing PIV Measurements Through the Lens of Data Clustering

Spatial and snapshot clustering approaches are presented and discussed for particle image velocimetry (PIV) data of high-Reynolds number uniform and buoyant jets and 4-and 7-bladed propeller wakes respectively. Data clustering is based on the k-means algorithm, along with the identification of the optimal number of clusters based on three metrics, namely the within-cluster sum of squares, average silhouette, and number of proper orthogonal decomposition (POD) modes required to resolve a desired variance. Spatial clustering for jets flow is based on three sets of clustering variables, namely cross-section velocity profiles, point-wise energy spectra, and pointwise Reynolds stress tensor components. Snapshot clustering of phase-locked propellers wake data is based on the vorticity with focus on tip vortices regions. POD and t-distributed stochastic neighbor embedding along with kernel density estimation are used to provide a twodimensional visualization of data clusters for assessment and discussion. The objective of this work is to lay the ground for a systematic data-clustering analysis of PIV data. The examples discussed show how clustering methods can help in achieving physical insights of complex fluid dynamics problems.