Extended mean flow analysis of the circular cylinder flow

TL;DR

This paper introduces an extended mean-flow eigenvalue analysis for circular cylinder flow, capturing interactions with second harmonics, leading to improved predictions of flow oscillation characteristics at high Reynolds numbers.

Contribution

It develops a novel extended mean-flow analysis that includes second-harmonic interactions, enhancing the understanding of nonlinear saturation mechanisms in laminar cylinder flow.

Findings

Identifies two zero-growth-rate eigenvalues in the flow.

High-frequency eigenmode predicts flow frequency and structure more accurately.

Enhanced analysis improves understanding of flow limit cycles at high Reynolds numbers.

Abstract

A new eigenvalue analysis is developed and applied to the circular cylinder laminar flow configuration to investigate the various mechanisms at play in the nonlinear saturation of perturbations yielding to limit cycles for supercritical values of the Reynolds number. Unlike the mean-flow analysis, which only accounts for the interaction of the first-harmonic of the time-periodic flow with its mean-flow, the so-called extended mean-flow analysis also accounts for its interaction with the second-harmonic. The results reveal the existence of two eigenvalues both having a growth rate exactly equal to zero. The high-frequency eigenmode gives better estimations of the frequency and spatial structure of the first-harmonic than the marginal modes obtained with the mean-flow analysis, especially when the Reynolds number is increased.