Linear Global Stability Analysis of a Laminar Flow Around a Circular Body

Abstract

The paper presents the linear global stability analysis of a laminar flow around a circular body at different Reynolds numbers. The results are validated against the literature. The numerical simulations are carried out for both steady state (time independent) and unsteady state (time dependent) flow regimes using the FreeFEM++ software. In the unsteady regime, the flow becomes unsteady when it reached a critical Reynolds number of $\sim 46.5$ and a vortex shedding develops downstream the cylinder. The results of linear global stability analysis for both steady and mean flows are presented. The eigenvalues obtained from the linear stability analysis were compared to the data available in literature. The linear stability analysis of the steady flow correctly predicted the growth rate of the instabilities, but it failed to predict the frequency. The linear stability analysis of the mean flow correctly predicted the frequency of the instabilities, but it underestimated the growth rates. At last, the sensitivity maps of the wavemaker were computed to determine the zone which is more receptive to a modification of the base flow to control the onset of the instability.