Instability of a Vortex Column Due to Turbulence Generated Axial Flow
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Axial flow generated by turbulence on an initially two-dimensional vortex column, the Lamb-Oseen vortex, is studied theoretically and by direct numerical simulation of the Navier-Stokes equations. Azimuthally wrapped filaments of opposite circulations, discussed for the case of two oppositely oriented filaments, advect radially in opposite directions, leading to radial separation of the filaments and net axial flow on the vortex axis. Axial velocity is found to grow as t^(5/2) from the simulation results, closely matching the analytically determined growth rate. Derivation of the axial flow magnitude predicts the onset of instability due to axial flow via the q (≡peak azimuthal velocity/peak axial velocity) criterion. Simulation results show (limited) renewed growth when q decreases below the unstable limit, likely dominating the previously discussed parent-offspring hairpin vortex mechanism for regenerative growth and suggesting possible breakup of the initially normal mode stable vortex at higher vortex Reynolds number due to ambient turbulence.