Interaction between trefoil knotted flame and vortex

We study the interaction between knotted flame and vortex tubes using the direct numerical simulation. A 3D configuration of the flame-vortex interaction is proposed. The premixed flame is initially located within a vortex tube with the same trefoil knotted centerline, and it propagates outward and interacts with the knotted vortex tube. This configuration is able to investigate the flame extinction, flame-flame interaction, and suppression of the vortex reconnection. Compared to the nonreacting knotted vortex tube, the flame-vortex interaction modifies the helicity dynamics and the morphology of vortex and flame tubes. The combustion generally decreases the helicity due to enhanced viscosity effects, but also slightly increases the helicity during a short time when the local extinction occurs. The nonmonotonic variation of the helicity results from the unsymmetrical flame propagation along the vortex axis after the local flame extinction. Moreover, some parts of the flame and vortex tubes are flattened through the early evolution. The flattening is primarily due to the baroclinic effects arising from the misalignment between the local density gradient and the nonlocal pressure gradient that strongly depends on the flame-vortex configuration.