Towards extreme event prediction of turbulent flows with quantized local reduced-order models

TL;DR

This paper introduces quantized local reduced-order models (ql-ROMs) for turbulent flows, enabling accurate, stable, and interpretable analysis and prediction of extreme events by combining data-driven clustering with Galerkin projection.

Contribution

The work develops a novel ql-ROM framework that accurately captures turbulent dynamics and predicts extreme events, integrating clustering with local POD bases for stability and interpretability.

Findings

ql-ROM accurately reproduces kinetic energy and dissipation statistics

Dissipation bursts linked to localized energy transfer in flow structures

Framework offers interpretable insights into turbulence dynamics

Abstract

This work develops quantized local reduced-order models (ql-ROMs) of the turbulent Minimal Flow Unit (MFU) for the analysis and interpretation of intermittent dissipative dynamics and extreme events. The ql-ROM combines data-driven clustering of the flow state space with intrusive Galerkin projection on locally defined Proper Orthogonal Decomposition (POD) bases. This construction enables an accurate and stable low-dimensional representation of nonlinear flow dynamics whilst preserving the structure of the governing equations. The model is trained on direct numerical simulation data of the MFU. When deployed, the ql-ROM is numerically stable for long-term integration, and correctly infers the statistical behavior of the kinetic energy and dissipation observed of the full-order system. A local modal energy-budget formulation is employed to quantify intermodal energy transfer and viscous dissipation within each region of the attractor. The analysis reveals that dissipation bursts correspond to localized energy transfer from streamwise streaks and travelling-wave modes toward highly dissipative vortical structures, consistent with the self-sustaining process of near-wall turbulence. Beyond reduced modeling, the ql-ROM framework provides a pathway for the reduced-space characterization and potential prediction of extreme events. ql-ROM offer an interpretable and computationally efficient framework for the analysis and prediction of extreme events in turbulent flows.