Divide and Conquer: Cluster and manifold-based interpretation of complex flows

TL;DR

This paper introduces a novel framework that combines manifold learning and clustering to analyze complex flow dynamics by partitioning the domain into subregions with similar local behaviors, enabling detailed flow interpretation.

Contribution

The paper presents an innovative method that uses nonlinear manifold learning and unsupervised clustering to automatically partition flow domains and describe local dynamics, improving upon existing global analysis techniques.

Findings

Successfully applied to fluidic pinball flow data

Identifies vortex dynamics not captured by global models

Automates domain partitioning for flow analysis

Abstract

We propose a framework for a global description of the dynamics of complex flows via clusterized spatial representations of the flow, isolating and identifying local dynamics, retrieving different Space-Time Cluster-Based Network Models (ST-CNMs). 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. From these, 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 modeling. 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, 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.