Data-driven identification of the spatio-temporal structure of turbulent flows by streaming Dynamic Mode Decomposition

TL;DR

Streaming Dynamic Mode Decomposition (sDMD) efficiently extracts dominant spatio-temporal structures from large turbulent flow datasets, offering a resource-effective alternative to classical DMD with reliable accuracy.

Contribution

This paper demonstrates the application of sDMD to turbulent flows, showing its effectiveness in identifying key flow structures with reduced computational resources.

Findings

sDMD reliably reproduces dominant flow features

sDMD requires less computational resources than classical DMD

sDMD effectively separates structures of different frequencies and scales

Abstract

Streaming Dynamic Mode Decomposition (sDMD) (Hemati et al., Phys. Fluids 26(2014)) is a low-storage version of Dynamic Mode Decomposition (DMD) (Schmid, J. Fluid Mech. 656 (2010)), a data-driven method to extract spatio-temporal flow patterns. Streaming DMD avoids storing the entire data sequence in memory by approximating the dynamic modes through incremental updates with new available data. In this paper, we use sDMD to identify and extract dominant spatio-temporal structures of different turbulent flows, requiring the analysis of large datasets. First, the efficiency and accuracy of sDMD are compared to the classical DMD, using a publicly available test dataset that consists of velocity field snapshots obtained by direct numerical simulation of a wake flow behind a cylinder. Streaming DMD not only reliably reproduces the most important dynamical features of the flow; our calculations also highlight its advantage in terms of the required computational resources. We subsequently use sDMD to analyse three different turbulent flows that all show some degree of large-scale coherence: rapidly rotating Rayleigh--B\'enard convection, horizontal convection and the asymptotic suction boundary layer. Structures of different frequencies and spatial extent can be clearly separated, and the prominent features of the dynamics are captured with just a few dynamic modes. In summary, we demonstrate that sDMD is a powerful tool for the identification of spatio-temporal structures in a wide range of turbulent flows.