Late time vortex dynamics for a coherent structure interacting with fine-scale turbulence

The vortex dynamics of perturbations to a coherent vortex column with fine-scale turbulence induced axial flow are examined using direct numerical simulation. Turbulence forms into azimuthally oriented filaments, which naturally results in axial flow as the filaments self-advect. Axial flow ($W)$ modifies vorticity generation in two ways: 1) the radial gradient of $W$ causes radial perturbation vorticity to tilt into the axial direction; and 2) axial perturbation vorticity tilts mean azimuthal vorticity (the vortical equivalent of $W)$ into the radial direction. Given the cycle of radial and axial perturbation vorticity generation, with the concomitant generation of azimuthal vorticity by the column's mean strain, this provides a physical explanation for instability due to axial flow (i.e. instability of the Batchelor or $q$-vortex, where $q$ is the ratio of peak azimuthal to peak axial velocities). Via this interpretation, the role of non-axisymmetric azimuthal modes in $q$-vortex instability is explained. Vorticity generation due to axial flow is explored using a simplified perturbation consisting of two, antiparallel helical vortex threads encircling a vortex column, which results in late time vorticity generation and energy production.