Onset of turbulence and layering in stratified columnar Taylor–Green vortices

We use direct numerical simulations to examine the onset of stratified turbulence triggered by the zigzag instability recently identified in columnar Taylor–Green vortices (Guo et al. 2024, J. Fluid Mech., vol. 997, A34) and its role in layer formation within the flow. The study focuses on Froude numbers 0.125 Fr 2.0 and Reynolds numbers Re ranging from 800 to 3200. The breakdown of the freely evolving vortex array is driven by local density overturns, combining shear and convective mechanisms initiated by the primary zigzag instability. Our results show a linear relationship between the peak buoyancy Reynolds number Reb , driven by the zigzag instability, and Re\, Fr² . When the flow does not exhibit local shear or convective instability, the value of Reb falls below unity. Both density and momentum layers arise from the zigzag instability: horizontal velocity layers are strong and persistent, while density layers are weaker and more transient. The vertical scale of the mean shear layers increases with Fr for Fr 1 , shows weak dependence on Re , and agrees well with the length scale associated with the fastest-growing linear mode of the zigzag instability. Further analysis in the sorted buoyancy coordinate highlights the role of density overturns caused by the zigzag instability in forming buoyancy layers during the transition to turbulence.