Baroclinic Critical Layers and the Zombie Vortex Instability in Rotating Stratified Cylindrical Flows

We investigate finite-amplitude instabilities of a Lamb–Oseen vortex in a rotating, vertically stratified fluid, with particular focus on the Zombie Vortex Instability (ZVI) in cylindrical geometry. ZVI has been previously observed in unbounded Cartesian domains with constant horizontal shear, where it originates from baroclinic critical layers that roll up into vortices, replicate, and ultimately form space-filling, sustained turbulence. While past studies have advanced the understanding of critical-layer dynamics, the precise mechanism by which finite-amplitude perturbations trigger ZVI and lead to self-sustained turbulence remains unresolved. Additionally, the feasibility of observing ZVI in laboratory settings is an open and active question.

In this work, we perform fully nonlinear simulations using a pseudo-spectral code in an unbounded cylindrical domain. The Lamb–Oseen vortex, used as the base flow, supports both barotropic and baroclinic critical layers and introduces important differences from the Cartesian case, including modified critical-layer locations due to azimuthal shear with radial variation and the quantization of azimuthal modes. These distinctions enable meaningful comparisons with horizontally sheared Cartesian flows and offer new insights into the underlying instability mechanisms.

Our objectives are to identify parameter regimes—specifically the Brunt–Väisälä frequency N and background rotation rate Ω—in which ZVI arises in cylindrical flows, and to assess whether such dynamics could eventually be explored in Taylor–Couette laboratory experiments. We also aim to gain further insight into the role of Rossby number in triggering the instability, the importance of wave resonance in ZVI development, and the spectral characteristics of ZVI-driven turbulence in cylindrical configurations.