Dynamics-based machine learning of transitions in Couette flow

TL;DR

This paper develops low-dimensional, data-driven models for flow transitions in plane Couette flow, capturing key dynamics on spectral submanifolds using minimal data, and accurately predicting transitions.

Contribution

It introduces a novel SSMLearn algorithm to construct reduced models on spectral submanifolds from limited transition data, improving flow transition predictions.

Findings

Models accurately predict transitions on spectral submanifolds.

Energy input/output rates effectively parametrize key dynamics.

Reduced models generalize to off-SSM transitions.

Abstract

We derive low-dimensional, data-driven models for transitions among exact coherent states (ECSs) in one of the most studied canonical shear flows, the plane Couette flow. These one- or two-dimensional nonlinear models represent the leading-order reduced dynamics on attracting spectral submanifolds (SSMs), which we construct using the recently developed SSMLearn algorithm from a small number of simulated transitions. We find that the energy input and output rates provide efficient parametrizations for the most important SSMs. By restricting the dynamics to these SSMs, we obtain reduced-order models that also reliably predict nearby, off-SSM transitions that were not used in their training.