Floquet analyses of complex 3D flows

Stability analyses of two-dimensional flows have become quite common during the past two decades. With increasing computational power, the stability of three-dimensional flows is feasible as well. However, much less attention has been paid to the stability of time-periodic flows. Such flows may arise due to harmonic forcing or naturally via a Hopf bifurcation. Furthermore, as the control parameter (e.g., Reynolds number) varies, these time-periodic dynamics may themselves become linearly unstable. Investigating these stability properties falls into the framework of Floquet theory.

This talk illustrates how an existing time-stepping code can be adapted to compute unstable periodic orbits and study their stability. It relies on nekStab, our recent open-source toolbox for large-scale stability analyses in Nek5000. After describing the algorithms implemented in nekStab, its capabilities will be illustrated on three examples: the flow past a tandem of side-by-side cylinders, the harmonically forced axial jet, and a three-dimensional pulsated jet in a cross-boundary layer flow.