Divide and conquer complex flows. Part I: cluster and manifold-based local analysis

Abstract

This work is a two-part study on the description and prediction of complex fluid flows through the partitioning of the flow domain. In this first part, we propose a framework for a global description of the dynamics of complex flows via clustered spatial representations of the flow, isolating and identifying local dynamics, retrieving different \acp{ST-CNM}. The key enabler is the partitioning of the domain based on a nonlinear manifold learning approach, in which spatial points are clustered based on the similarity of their dynamics, as observed in their compact embedding in manifold coordinates. The method receives as input time-resolved flow fields. The spatial manifold is computed through isometric mapping applied to the vorticity time histories at each spatial location. An unsupervised clustering method, applied in the manifold space, partitions the full flow domain into subdomains. The dynamics of each subdomain are then described with cluster-based modelling. The method is demonstrated on two flow-field datasets obtained with a direct numerical simulation of a fluidic pinball under periodic forcing and with two-dimensional particle image velocimetry measurements of a transitional jet flow. The spatial manifold-based flow partitioning identifies regions with similar dynamics in an automated way. For both cases, \ac{ST-CNM} identifies local dynamics that are not captured by a global approach. In particular, vortex shedding and vortex pairing dynamics are isolated in the jet flow experiment. The proposed fully automated domain partitioning method will benefit the structural description of controlled flows and unveil the actuation mechanisms at play.