Data-driven time-dependent bases for turbulent airfoil wake-extreme vortex gust interactions

TL;DR

This paper introduces a data-driven, time-dependent modal analysis framework to study turbulent wake interactions with extreme gusts on airfoils, revealing how gust intensity affects flow structures and recovery dynamics.

Contribution

It develops a novel approach using time-varying bases and closed-form evolution equations to analyze turbulent airfoil wake-gust interactions without full historical data storage.

Findings

Stronger gusts increase energy in secondary modes.

Larger energy gaps in leading modes indicate faster flow recovery.

Transient lift dynamics correlate with modal energy evolution.

Abstract

We analyze interactions between turbulent airfoil wake and an extremely strong gust using a data-driven framework with time-dependent bases. The current approach represents each snapshot with time-varying bases consisting of two-dimensional in-plane modes and one-dimensional spanwise modes, together with a reduced covariance matrix. We derive closed-form evolution equations for these time-varying components and advance them over time, requiring only a small rolling window and avoiding full-history storage. Applied to extreme vortex gust-airfoil interaction at Re=5000, we examine how in-plane modes and their associated energy level evolve across gust conditions of varying intensity and size. Before impingement, the first in-plane mode dominates; after impingement, the second mode gains energy_amplified by stronger/larger gusts. A larger leading-mode energy gap implies coherent structure and faster recovery; a smaller gap with slower decay indicates richer multiscale activity and delayed re-stabilization. These trends follow the transient lift dynamics as well, with higher amplitude and more oscillations indicated by a rise in the leading singular values. This work provides an interpretable, time-varying data-driven modal analysis of extreme gust encounter.