Data-driven oscillator model for multi-frequency turbulent flows

TL;DR

This paper introduces a data-driven oscillator modeling framework for multi-frequency turbulent flows, enabling accurate long-term predictions and deeper understanding of complex flow dynamics.

Contribution

It develops a novel method using autoencoders and neural networks to extract and model oscillators from turbulent flow data, addressing multi-frequency chaos.

Findings

Oscillators capture dominant large-scale flow features.

Model accurately forecasts turbulent flow oscillations over long periods.

Method applicable to complex three-dimensional turbulent flows.

Abstract

The complex dynamics of high-dimensional oscillatory flows can be simplified using phase-reduction analysis, providing a deeper understanding of the flow response to external perturbations. Although phase-based modeling and analysis have been utilized in recent studies on oscillatory fluid flows, their usages are still limited to single-frequency flows due to difficulties in addressing chaotic characteristics induced by multiple frequencies of turbulent flows. In order to overcome this limitation, we propose a data-driven framework that models the dynamics of multi-frequency turbulent flows based on a set of oscillators. The representative oscillators are extracted from the flow field data by training specially designed autoencoders. The oscillator dynamics are modeled through a machine-learning technique using neural networks to accurately predict the multi-frequency oscillatory behavior of turbulent flows. We verify the oscillator-based model of the multi-frequency turbulent flow by applying the proposed data-driven method to the three-dimensional supersonic turbulent flow over a cavity. We show that the extracted oscillators represent the dominant large-scale flow features and reflect the physical characteristics of the turbulent cavity flow. The data-driven oscillator dynamics model accurately forecasts the oscillatory behavior of the turbulent cavity flow for a long period. The proposed data-driven method for reduced-order modeling of turbulent flows with oscillators will enable deeper investigations of perturbation dynamics and control of turbulent flows.