Local stability analysis of homogeneous and stratified Kelvin-Helmholtz vortices

We perform a three-dimensional short-wavelength linear stability analysis of numerically simulated two-dimensional Kelvin-Helmholtz vortices in homogeneous and stratified environments at a fixed Reynolds number of Re = 300. For the homogeneous case, the elliptic instability at the vortex core dominates at early times, before being taken over by the hyperbolic instability at the vortex edge. For the stratified case of Richardson number Ri = 0.08, the early-time instabilities comprise a dominant elliptic instability at the core and a hyperbolic instability influenced strongly by stratification at the vortex edge. At intermediate times, the local approach shows a new branch of (convective) instability that emerges at the vortex core and subsequently moves towards the vortex edge. A few more convective instability bands appear at the vortex core and move away, before coalescing to form the most unstable region inside the vortex periphery at large times. In addition, the stagnation point instability is also recovered outside the periphery of the vortex at intermediate times. The dominant instability characteristics from the local approach are shown to be in good qualitative agreement with the results based on global instability studies for both homogeneous and stratified cases. A systematic study of the dependence of the dominant instability characteristics on Ri is then presented. While Ri = 0.1 is identified as most unstable (with convective instability being dominant), another growth rate maximum at Ri = 0.025 is not far behind (with the hyperbolic instability influenced by stratification being dominant). Finally, the local stability approach is shown to predict the potential orientation of the flow structures that would result from hyperbolic and convective instabilities, which is found to be consistent with three-dimensional numerical simulations reported previously.

Automated summary

This study investigates the stability of two-dimensional Kelvin-Helmholtz vortices using numerical simulations. The results show that different types of instabilities occur at the core and the edge of the vortices, and stratification strongly influences the instability at the vortex edge. The dependence of the dominant instability characteristics on the Richardson number is systematically studied. The local stability approach is able to predict the orientation of flow structures resulting from different instabilities, consistent with previous three-dimensional numerical simulations.