Spectral proper orthogonal decomposition of harmonically forced turbulent flows

TL;DR

This paper extends spectral proper orthogonal decomposition to cyclostationary turbulent flows, enabling analysis of flows with periodic statistical variations, demonstrated through models and turbulent jet examples.

Contribution

It introduces cyclostationary SPOD (CS-SPOD), connecting it to harmonic resolvent analysis and providing an efficient computational algorithm.

Findings

CS-SPOD effectively captures periodic flow structures.

Theoretical link between CS-SPOD and harmonic resolvent analysis.

Demonstrated application on turbulent jet and Ginzburg-Landau model.

Abstract

Many turbulent flows exhibit time-periodic statistics. These include turbomachinery flows, flows with external harmonic forcing, and the wakes of bluff bodies. Many existing techniques for identifying turbulent coherent structures, however, assume the statistics are statistically stationary. In this paper, we leverage cyclostationary analysis, an extension of the statistically stationary framework to processes with periodically varying statistics, to generalize the spectral proper orthogonal decomposition (SPOD) to the cyclostationary case. The resulting properties of the cyclostationary SPOD (CS-SPOD for short) are explored, a theoretical connection between CS-SPOD and the harmonic resolvent analysis is provided, simplifications for the low and high forcing frequency limits are discussed, and an efficient algorithm to compute CS-SPOD with SPOD-like cost is presented. We illustrate the utility of CS-SPOD using two example problems: a modified complex linearized Ginzburg-Landau model and a high-Reynolds-number turbulent jet.