Zigzag instability of columnar Taylor-Green vortices in a strongly stratified fluid*

We investigate the dynamics of a columnar Taylor-Green vortex array under strong stratification, focusing on Froude numbers from 0.125 to 1.0, to identify and understand the primary instabilities leading to the vortices' breakdown. Linear stability analysis reveals that the fastest-growing vertical wavenumber scales with 1/Fr, while the dimensionless growth rate remains approximately constant. The most unstable eigenmode, identified as the mixed hyperbolic mode by Hattori et al. (J. Fluid Mech. vol. 909, 2021, A4), bears significant similarities to the zigzag instability first discovered by Billant and Chomaz (J. Fluid Mech. vol. 418, 2000, pp. 167-188). Direct numerical simulations confirm that the zigzag instability is crucial in amplifying initial random perturbations to finite amplitude, with the flow structure and modal growth rate consistent with the linear stability analysis. In particular, the characteristic vertical length scale of turbulence matches that of the fastest-growing linear mode. These findings underscore the broader relevance of the zigzag instability mechanism beyond its initial discovery in vortex pairs, demonstrating its role in facilitating direct energy transfer from vertically uniform vortical motions to a characteristic wavenumber inversely proportional to Fr in strongly stratified flows.