Energetics of instability modes in the cylinder wake

This study investigates the perturbation kinetic energy budget of the instability modes in the circular cylinder wake using the out-of-plane averaged perturbation kinetic energy (PKE) equation. This equation relates to the instability growth rates predicted through linear stability analysis techniques and provides a means to understand the sources through which the linear modes grow on the two-dimensional base flow. In this study, the linear modes A and B are studied at their corresponding transition Reynolds number. The most dominant rate of production terms contributing to the mode A and B instability growth are those derived from cross-flow gradients of the base flow velocity, although the terms for mode B occur at higher rates than those for mode A. The locus of the regions with high production rates within the flow field (concerning the sum of the two dominant production terms) shows that the perturbations for mode A develop most rapidly in the elliptical core of the forming vortex, while those for mode B are amplified most in the interface between the two forming vortices, reaching a maximum when the vortex sheds from the cylinder. The mode A unstable flow then describes weak secondary regions of production within the elliptical vortex cores further downstream, and is a feature absent in mode B.