Dynamics-based machine learning of transitions in Couette flow

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.

Accepted version

References in corpus (7)

• Lower branch coherent states in shear flows: transition and control
• Data-Driven Modeling and Prediction of Non-Linearizable Dynamics via Spectral Submanifolds
• How to Compute Invariant Manifolds and their Reduced Dynamics in High-Dimensional Finite-Element Models
• Laminar-turbulent boundary in plane Couette flow
• Heteroclinic connections in plane Couette flow
• Nonlinear analysis of forced mechanical systems with internal resonance using spectral submanifolds, Part I: Periodic response and forced response curve
• Data-driven Nonlinear Model Reduction to Spectral Submanifolds in Mechanical Systems