Breakup and Reorganization of a Turbulent Batchelor Vortex

The breakup and reorganization, i.e. recombination of the vorticity filaments from the disrupted core into a columnar vortex due to pairing, merging and viscous diffusion, of a Batchelor vortex is studied using Smagorinsky model Large Eddy Simulation (LES). At Reynolds numbers (vortex circulation/viscosity) up to 500,000, an unstable Batchelor vortex embedded in random turbulence breaks up in to vorticity filaments. These filaments tend to form dipoles and advect away from the original axis due to the swirling jet flow. Regardless of the strength of the jet flow causing the instability, filaments near the core are nearly axial, and thus eventually undergo mutual rotation and eventually pair, merge and reorganize into a columnar structure. The effect of the core reorganization on vortex decay – decrease in the peak azimuthal velocity and increase in the radius of the peak azimuthal velocity – is discussed for the potential to model vortex evolution and predict the time to “safe” vortex states. Evolutions of the Oseen vortex embedded in turbulence as well as vortices excited with linear transient growth optimal perturbation eigenfunctions are compared to the Batchelor vortex cases to illustrate the changes to vortex evolution, breakup and reorganization with increasing axial flow.