Mechanisms of perturbation growth and turbulence evolution in a columnar vortex

Some evolutionary mechanisms of coherent structures in turbulence are revealed by computations of (I) core dynamics (CD) in a vortex subjected to external straining; and (II) a vortex column embedded in finer-scaled turbulence.; (I) CD evolves as a standing wave that grows when the vortex is externally strained and is damped when not. The instability results from resonance---at discrete wavelengths where the CD oscillation frequency matches the vortex's angular velocity---causing strain-vorticity locking.; (II) Vortex-turbulence interaction---fundamental to turbulence modeling and to flows such as the aircraft wake---exhibits two distinct regions: (a) a vortex core with intense wave motions; and (b) a turbulent annulus containing coherent fine-scale filaments organized into dipoles. Mean momentum transport by the filaments causes an overshoot of the circulation profile, rendering the vortex centrifugally unstable, but having little effect on enhancing turbulence production. The turbulent vortex, remarkably, decays at a viscous rate: a consequence of core wave motions, which, though intense, generate little Reynolds stress. No self-similar state---assumed in theories---is found.; Core fluctuation amplification---observed in vortex-turbulence interaction---is via transient growth: algebraic perturbation growth in a "stable" vortex. Energetically "optimal" perturbations---attaining up to a thousand-fold amplification at moderate vortex Reynolds numbers, Re ∼ 104---grow via two inviscid mechanisms: (a) two-dimensional perturbations with "positive-tilt" streamlines (contributing positive Reynolds stress) grow until the mean swirl transforms the streamlines to predominantly "negative tilt"; (b) three-dimensional perturbations grow through the tilting of radial vorticity to azimuthal, and concomitant vortex stretching. While the mean strain amplifies perturbations, mean vorticity promotes wave motions, which arrest growth. Strong transient growth of bending waves---through resonance with external filaments---explains their appearance on a vortex in a turbulent field. Nonlinear growth of optimal modes causes significant core distortion and, likely, core transition---hence rapid vortex decay---in high-Re practical flows, such as the aircraft trailing vortex. The failure of turbulence models to capture transient growth may be why predicted and experimentally-observed decay rates of turbulent vortices differ.