Tripolar Instability of a Strained Lamb-Oseen Vortex

Our goal is to investigate the stability of a Lamb-Oseen vortex under tripolar straining. The motivation for our study is that the hub vortex formed in turbomachinery with three blades experiences tripolar straining from the surrounding vortices and this can potentially lead to instability and the onset of turbulence. Although the curvature and elliptic instabilities of a Lamb-Oseen vortex and the multipolar instability of a Rankine vortex are well-studied, the multipolar instability of a Lamb-Oseen vortex remains under-explored numerically and theoretically. In this study, we present the evidence for the tripolar instability through direct numerical simulations (DNS) by performing linear stability analysis for a basic flow of a hub Lamb-Oseen vortex strained by three satellite Lamb-Oseen vortices. We demonstrate that for a specific combination of resonant azimuthal wavenumbers of 1 and -2, instability occurs only for some resonant axial wavenumbers. Unstable growth rates are also computed theoretically and compared to the DNS results.