Azimuthal Vortex Instability in Turbulent Jets

An axisymmetrically forced initially-laminar jet at a Reynolds number $Re = \rho U_{j}D/\mu = 50000$ is investigated to identify the presence of Widnall instability. The Widnall instabilty is a short-wave azimuthal instability that grows on isolated vortex rings. Using visualizations and Q-criterion, we identify a primary vortex rollup associated with the Kelvin-Helmholtz response of the jet to forcing and secondary azimuthal perturbations that grow on the rolled-up cores that have characteristics of the Widnall instability. The presence of this instability in forced transitional jets was previously identified by Monkewitz et al [1], and our numerical simulations provide direct evidence that supports and extends those findings. Conditional averaging highlights the dominance of higher azimuthal wavenumbers, particularly $m=16$, which contribute to the wavy deformation of the vortex rings in the initial part of shear layer. As the core of the ring thickens further downstream, lower azimuthal wavenumbers become dominant. Conditional space-time proper orthogonal decomposition is used to track the evolution of the perturbations. The leading mode captures both the growth of azimuthal distortions and the gradual spacing of the rings as they evolve downstream. Notably, the vortex rings develop a four-lobed structure within $ x \leq 5$ of the shear layer, which closely matches the most amplified wavenumber predicted by the Widnall and Tsai dispersion relation [2], providing strong evidence of Widnall instability. As this instability grows on the vortex ring, it generates counter-rotating streamwise vortices that induce a lift-up effect, resulting in enhanced entrainment and the formation of streaks.