On Some Modal Implications of the Dynamic Mode Decomposition Through the Lens of a Subcritical Prism Wake

TL;DR

This paper explores the modal implications of Dynamic Mode Decomposition (DMD) in fluid mechanics, demonstrating its ability to accurately and insightfully characterize flow phenomena in a subcritical prism wake.

Contribution

It provides a detailed analysis of the dominant DMD modes in a shear flow, linking modal structures to physical flow features and demonstrating DMD's effectiveness in fluid dynamics.

Findings

DMD accurately captures mean flow and vortex structures.

Modes correspond to specific flow phenomena like vortex roll-up and turbulence.

DMD offers physically insightful reduced-order models for complex flows.

Abstract

The Dynamic Mode Decomposition (DMD) is a Koopman-based algorithm that straightforwardly isolates individual mechanisms from the compound morphology of direct measurement. However, many may be perplexed by the messages the DMD structures carry. This work investigates the modal implications of the DMD/Koopman modes through the prototypical subcritical free-shear flow over a square prism. It selected and analysed the fluid mechanics and phenomenology of the ten most dominant modes. The results showed that the reduced-order description is morphologically accurate and physically insightful. Mode 1 renders the mean-field. Modes 2 depicts the roll-up of the Strouhal vortex. Mode 3 delineates the Bloor-Gerrard vortex resulting from the Kelvin-Helmholtz instability inside shear layers, its superposition onto the Strouhal vortex, and the concurrent flow entrainment. Modes 4, 5, 7, 8, and 9 portray the harmonic excitation. Modes 6 and 10 describe the low-frequency shedding of turbulent separation bubbles (TSBs) and turbulence production, respectively, which contribute to the beating phenomenon in the lift time history and the flapping motion of shear layers. Finally, this work demonstrates the capability of the DMD in providing insights into similar fluid problems. It also serves as an excellent reference for an array of other nonlinear systems.