# Networked oscillator based modeling and control of unsteady wakes

## TL;DR

This paper introduces a networked oscillator model for analyzing and controlling unsteady wake flows, capturing energy exchanges among flow modes to improve flow control and reduce drag.

## Contribution

It presents a novel networked oscillator framework that models modal interactions in unsteady flows, enabling effective control strategies for wake suppression.

## Key findings

- Networked oscillator model outperforms empirical Galerkin models in capturing modal dynamics.
- The approach successfully suppresses wake unsteadiness and reduces drag in flow over a circular cylinder.
- Linear regression effectively identifies energy transfer networks among flow modes.

## Abstract

A networked oscillator based analysis is performed for periodic bluff body flows to examine and control the transfer of kinetic energy. Spatial modes extracted from the flow field with corresponding amplitudes form a set of oscillators describing unsteady fluctuations. These oscillators are connected through a network that captures the energy exchanges amongst them. To extract the network of interactions among oscillators, amplitude and phase perturbations are impulsively introduced to the oscillators and the ensuing dynamics are analyzed. Using linear regression techniques, a networked oscillator model is constructed that reveals energy transfers and phase interactions among the modes. The model captures the nonlinear interactions amongst the modal oscillators through a linear approximation. A large collection of system responses are aggregated into a network model that captures interactions for general perturbations. The networked oscillator model describes the modal perturbation dynamics better than the empirical Galerkin reduced-order models. A model-based feedback controller is then designed to suppress modal amplitudes and the resulting wake unsteadiness leading to drag reduction. The strength of the proposed approach is demonstrated for a canonical example of two- dimensional unsteady flow over a circular cylinder. The present formulation enables the characterization of modal interactions to control fundamental energy transfers in unsteady vortical flows.